Essential Statistics
Essential Statistics
2nd Edition
ISBN: 9781259570643
Author: Navidi
Publisher: MCG
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Chapter 4, Problem 10RE

a.

To determine

Compute the probability that selected patient is a woman.

a.

Expert Solution
Check Mark

Answer to Problem 10RE

The probability that selected patient is a woman is 0.4035.

Explanation of Solution

Calculation:

It is given that 644,404 patients were hospitalized for heart attack. The table provides idea about number of male and female patients hospitalized in each age group.

The probability of the event A can be obtained by the formula:

P(A)=Number of outcomes in ANumber of outcomes insample space

Here, event A denotes that selected patient is a woman. Among the 644,404 patients, 260,005 of them are woman.

Substitute 260,005 for “number of outcomes in A” and 644,404 for “Number of outcomes in sample space” in the probability formula.

Therefore,

P(A)=260,005644,404=0.40348=0.4035

Thus, the probability that selected patient is a woman is 0.4035.

b.

To determine

Compute the probability that selected patient is aged 45-64.

b.

Expert Solution
Check Mark

Answer to Problem 10RE

The probability that selected patient is aged 45-64 is 0.3647.

Explanation of Solution

Calculation:

Event B denotes that selected patient is aged 45-64. Among the 644,404 patients,  235,006 of them are woman.

Substitute 235,006 for “number of outcomes in B” and 644,404 for “Number of outcomes in sample space” in the probability formula.

Therefore,

P(B)=235,006644,404=0.36468=0.3647

Thus, the probability that selected patient is aged 45-64 is 0.3647.

c.

To determine

Compute the probability that selected patient is a woman and aged 45-64.

c.

Expert Solution
Check Mark

Answer to Problem 10RE

The probability that selected patient is a woman and aged 45-64 is 0.1066.

Explanation of Solution

Calculation:

Event A denotes that selected patient is a woman and event B denotes that selected patient is aged 45-64. Event ‘A and B’ denote that selected patient is a woman and aged 45-64.

Among the 644,404 patients, 68,666 of them are woman and aged 45-64.

Substitute 68,666 for “number of outcomes in ‘A and B’” and 644,404 for “Number of outcomes in sample space” in the probability formula.

Therefore,

P(Aand B)=68,666644,404=0.10655=0.1066

Thus, the probability that selected patient is a woman and aged 45-64 is 0.1066.

d.

To determine

Compute the probability that selected patient is a woman or aged 45-64.

d.

Expert Solution
Check Mark

Answer to Problem 10RE

The probability that selected patient is a woman or aged 45-64 is 0.6616.

Explanation of Solution

Calculation:

Event A denotes that selected patient is a woman and event B denotes that selected patient is aged 45-64. Event ‘A and B’ denote that selected patient is a woman and aged 45-64.

The probability that selected patient is a woman or aged 45-64 can be expressed as, P(Aor B).

General Addition rule:

For any two events A and B the general addition rule states that

P(Aor B)=P(A)+P(B)P(Aand B)

From parts (a), (b), and (c), P(A)=0.4035P(B)=0.3647,andP(Aand B)=0.1066.

Substitute these values in the general addition rule.

Therefore,

P(Aor B)=0.4035+0.36470.1066=0.6616

Thus, the probability that selected patient is a woman or aged 45-64 is 0.6616.

e.

To determine

Compute the probability that selected patient is a woman given that the patient is aged 45-64.

e.

Expert Solution
Check Mark

Answer to Problem 10RE

The probability that selected patient is a woman given that the patient is aged 45-64 is 0.2922.

Explanation of Solution

Calculation:

The formula for conditional probability is given by:

P(A|B)=P(AandB)P(B).

From part (b), P(B)=0.3647.

From part (c), P(Aand B)=0.1066.

Substitute these values in the formula for conditional probability.

Therefore,

P(A|B)=0.10660.3647=0.2922

Thus, the probability that selected patient is a woman given that the patient is aged 45-64 is 0.2922.

f.

To determine

Compute the probability that selected patient is aged 45-64 given that the patient is a woman.

f.

Expert Solution
Check Mark

Answer to Problem 10RE

The probability that selected patient is aged 45-64 given that the patient is a woman is 0.2641.

Explanation of Solution

Calculation:

The formula for conditional probability is given by:

P(B|A)=P(AandB)P(A).

From part (a), P(A)=0.4035.

From part (c), P(Aand B)=0.1066.

Substitute these values in the formula for conditional probability.

Therefore,

P(B|A)=0.10660.4035=0.2641

Thus, the probability that selected patient is aged 45-64 given that the patient is a woman is 0.2641.

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Chapter 4 Solutions

Essential Statistics

Ch. 4.1 - Prob. 11ECh. 4.1 - Prob. 12ECh. 4.1 - Prob. 13ECh. 4.1 - Prob. 14ECh. 4.1 - Prob. 15ECh. 4.1 - Prob. 16ECh. 4.1 - Prob. 17ECh. 4.1 - Prob. 18ECh. 4.1 - Prob. 19ECh. 4.1 - Prob. 20ECh. 4.1 - Prob. 21ECh. 4.1 - In Exercises 21–24, assume that a coin is tossed...Ch. 4.1 - Prob. 23ECh. 4.1 - In Exercises 21–24, assume that a coin is tossed...Ch. 4.1 - How probable is it? Someone computes the...Ch. 4.1 - Prob. 26ECh. 4.1 - Prob. 27ECh. 4.1 - Prob. 28ECh. 4.1 - Prob. 29ECh. 4.1 - 30. A coin flip: A fair coin is tossed three...Ch. 4.1 - 31. Empirical Method: A coin is tossed 400 times...Ch. 4.1 - Prob. 32ECh. 4.1 - Prob. 33ECh. 4.1 - Prob. 34ECh. 4.1 - Prob. 35ECh. 4.1 - Prob. 36ECh. 4.1 - Prob. 37ECh. 4.1 - Prob. 38ECh. 4.1 - 39. Get an education: The General Social Survey...Ch. 4.1 - Prob. 40ECh. 4.1 - 41. Hospital visits: According to the Agency for...Ch. 4.1 - Prob. 42ECh. 4.1 - Prob. 43ECh. 4.1 - Prob. 44ECh. 4.1 - Prob. 45ECh. 4.1 - Prob. 46ECh. 4.1 - Prob. 47ECh. 4.1 - Prob. 48ECh. 4.1 - Prob. 49ECh. 4.2 - Prob. 1CYUCh. 4.2 - Prob. 2CYUCh. 4.2 - Prob. 3CYUCh. 4.2 - Prob. 4CYUCh. 4.2 - Prob. 5ECh. 4.2 - In Exercises 5–8, fill in each blank with the...Ch. 4.2 - In Exercises 5–8, fill in each blank with the...Ch. 4.2 - In Exercises 5–8, fill in each blank with the...Ch. 4.2 - Prob. 9ECh. 4.2 - Prob. 10ECh. 4.2 - Prob. 11ECh. 4.2 - Prob. 12ECh. 4.2 - Prob. 13ECh. 4.2 - Prob. 14ECh. 4.2 - Prob. 15ECh. 4.2 - 16. If P (A) = 0.7, P (B) = 0.1, and A and B are...Ch. 4.2 - Prob. 17ECh. 4.2 - Prob. 18ECh. 4.2 - Prob. 19ECh. 4.2 - 20. If P(B) = 0.6, find P(Bc). Ch. 4.2 - Prob. 21ECh. 4.2 - Prob. 22ECh. 4.2 - Prob. 23ECh. 4.2 - Prob. 24ECh. 4.2 - Prob. 25ECh. 4.2 - In Exercises 25–30, determine whether events A and...Ch. 4.2 - Prob. 27ECh. 4.2 - Prob. 28ECh. 4.2 - In Exercises 25–30, determine whether events A and...Ch. 4.2 - In Exercises 25–30, determine whether events A and...Ch. 4.2 - In Exercises 31 and 32, find the complements of...Ch. 4.2 - In Exercises 31 and 32, find the complements of...Ch. 4.2 - Prob. 33ECh. 4.2 - Prob. 34ECh. 4.2 - Prob. 35ECh. 4.2 - 36. Sick computers: Let V be the event that a...Ch. 4.2 - Prob. 37ECh. 4.2 - Prob. 38ECh. 4.2 - Prob. 39ECh. 4.2 - 40. Statistics grades: In a statistics class of 30...Ch. 4.2 - Prob. 41ECh. 4.2 - Prob. 42ECh. 4.2 - Prob. 43ECh. 4.2 - Prob. 44ECh. 4.2 - Prob. 45ECh. 4.2 - Prob. 46ECh. 4.2 - 47. Mutual exclusivity is not transitive: Give an...Ch. 4.2 - 48. Complements: Let A and B be events. Express (A...Ch. 4.3 - 1. A person is selected at random from the...Ch. 4.3 - Prob. 2CYUCh. 4.3 - Prob. 3CYUCh. 4.3 - Prob. 4CYUCh. 4.3 - Prob. 5CYUCh. 4.3 - Prob. 6CYUCh. 4.3 - Prob. 7ECh. 4.3 - Prob. 8ECh. 4.3 - In Exercises 7–10, fill in each blank with the...Ch. 4.3 - In Exercises 7–10, fill in each blank with the...Ch. 4.3 - Prob. 11ECh. 4.3 - In Exercises 11–14, determine whether the...Ch. 4.3 - Prob. 13ECh. 4.3 - Prob. 14ECh. 4.3 - Prob. 15ECh. 4.3 - Prob. 16ECh. 4.3 - Prob. 17ECh. 4.3 - 18. Let A and B be events with P(A) = 0.5 and P(B)...Ch. 4.3 - 19. Let A and B be events with P (A) = 0.8, P(B) =...Ch. 4.3 - 20. Let A and B be events with P(A) = 0.3, P(B) =...Ch. 4.3 - Prob. 21ECh. 4.3 - Prob. 22ECh. 4.3 - Prob. 23ECh. 4.3 - Prob. 24ECh. 4.3 - Prob. 25ECh. 4.3 - Prob. 26ECh. 4.3 - Prob. 27ECh. 4.3 - In Exercises 27–30, assume that a student is...Ch. 4.3 - Prob. 29ECh. 4.3 - Prob. 30ECh. 4.3 - Prob. 31ECh. 4.3 - 32. Let A and B be events with P(A) = 0.6, P(B) =...Ch. 4.3 - Prob. 33ECh. 4.3 - Prob. 34ECh. 4.3 - Prob. 35ECh. 4.3 - Prob. 36ECh. 4.3 - Job interview: Seven people, named Anna, Bob,...Ch. 4.3 - Prob. 38ECh. 4.3 - Prob. 39ECh. 4.3 - 40. U.S. senators: The following table displays...Ch. 4.3 - Prob. 41ECh. 4.3 - Prob. 42ECh. 4.3 - Prob. 43ECh. 4.3 - Prob. 44ECh. 4.3 - Prob. 45ECh. 4.3 - Prob. 46ECh. 4.3 - Prob. 47ECh. 4.3 - Prob. 48ECh. 4.3 - Prob. 49ECh. 4.3 - Prob. 50ECh. 4.3 - Prob. 51ECh. 4.3 - Prob. 52ECh. 4.3 - Prob. 53ECh. 4.3 - Prob. 54ECh. 4.3 - Prob. 55ECh. 4.3 - Prob. 56ECh. 4.3 - Prob. 57ECh. 4.3 - Prob. 58ECh. 4.3 - Prob. 59ECh. 4.3 - Prob. 60ECh. 4.3 - Prob. 61ECh. 4.3 - Prob. 62ECh. 4.3 - Prob. 63ECh. 4.3 - Prob. 64ECh. 4.3 - Prob. 65ECh. 4.4 - When ordering a certain type of computer, there...Ch. 4.4 - Prob. 2CYUCh. 4.4 - Prob. 3CYUCh. 4.4 - Refer to Exercise 3. Two of the committee members...Ch. 4.4 - Prob. 5CYUCh. 4.4 - Refer to Exercise 5. Four of the eight students...Ch. 4.4 - Prob. 7ECh. 4.4 - In Exercises 7 and 8, fill in the blank with the...Ch. 4.4 - Prob. 9ECh. 4.4 - In Exercises 9 and 10, determine whether the...Ch. 4.4 - Prob. 11ECh. 4.4 - In Exercises 11–16, evaluate the factorial. 12. 5!Ch. 4.4 - Prob. 13ECh. 4.4 - Prob. 14ECh. 4.4 - Prob. 15ECh. 4.4 - In Exercises 11–16, evaluate the factorial. 16. 3!Ch. 4.4 - Prob. 17ECh. 4.4 - Prob. 18ECh. 4.4 - Prob. 19ECh. 4.4 - Prob. 20ECh. 4.4 - Prob. 21ECh. 4.4 - Prob. 22ECh. 4.4 - Prob. 23ECh. 4.4 - In Exercises 23–28, evaluate the combination. 24....Ch. 4.4 - Prob. 25ECh. 4.4 - In Exercises 23–28, evaluate the combination. 26....Ch. 4.4 - Prob. 27ECh. 4.4 - In Exercises 23–28, evaluate the combination. 28....Ch. 4.4 - Prob. 29ECh. 4.4 - Books: Josephine has six chemistry books, three...Ch. 4.4 - Prob. 31ECh. 4.4 - 32. Ice cream: A certain ice cream parlor offers...Ch. 4.4 - License plates: In a certain state, license plates...Ch. 4.4 - Committee: The Student Council at a certain school...Ch. 4.4 - Day and night shifts: A company has hired 12 new...Ch. 4.4 - Keep your password safe: A computer password...Ch. 4.4 - It’s in your genes: Human genetic material (DNA)...Ch. 4.4 - Choosing officers: A committee consists of ten...Ch. 4.4 - Prob. 39ECh. 4.4 - Blackjack: In single-deck casino blackjack, the...Ch. 4.4 - Prob. 41ECh. 4.4 - Prob. 42ECh. 4.4 - Prob. 43ECh. 4 - Fill in the blank: The probability that a fair...Ch. 4 - Prob. 2CQCh. 4 - Prob. 3CQCh. 4 - Prob. 4CQCh. 4 - Prob. 5CQCh. 4 - Prob. 6CQCh. 4 - Prob. 7CQCh. 4 - Prob. 8CQCh. 4 - Prob. 9CQCh. 4 - Prob. 10CQCh. 4 - Prob. 11CQCh. 4 - Prob. 12CQCh. 4 - Prob. 13CQCh. 4 - Prob. 14CQCh. 4 - Prob. 15CQCh. 4 - Prob. 1RECh. 4 - Prob. 2RECh. 4 - Prob. 3RECh. 4 - Blood types: Human blood may contain either or...Ch. 4 - Prob. 5RECh. 4 - Stop that car: A drag racer has two parachutes, a...Ch. 4 - Prob. 7RECh. 4 - Music to my ears: Jeri is listening to the songs...Ch. 4 - Prob. 9RECh. 4 - Prob. 10RECh. 4 - Rainy weekend: Sally is planning to go away for...Ch. 4 - Prob. 12RECh. 4 - Required courses: Refer to Exercise 12. Assume the...Ch. 4 - Bookshelf: Bart has six books: a novel, a...Ch. 4 - Bookshelf: Refer to Exercise 14. Bart chooses...Ch. 4 - Prob. 1WAICh. 4 - Prob. 2WAICh. 4 - Prob. 3WAICh. 4 - Prob. 4WAICh. 4 - Prob. 5WAICh. 4 - Prob. 6WAICh. 4 - Describe circumstances under which you would use a...Ch. 4 - Describe circumstances under which you would use a...Ch. 4 - The following table is a life table, reproduced...Ch. 4 - Prob. 2CSCh. 4 - Prob. 3CSCh. 4 - Prob. 4CSCh. 4 - Prob. 5CSCh. 4 - Prob. 6CSCh. 4 - Prob. 7CSCh. 4 - Prob. 8CSCh. 4 - Prob. 9CS
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