Given P(A) = 0.27, P(B) = 0.27, and P(B|A) = 0.21, are A and B independent or dependent?

Q: Given P(E) = 0.34, P(F) = 0.36, and P(E and F) = 0.17, what is P(E or F)?

A: Solution: From the given information,

Q: Given P(E or F) = 0.60, P(F) = 0.43, and P(E and F) = 0.11, what is P(E)?

A: Given  P(E or F) = 0.60, P(F) = 0.43, and P(E and F) = 0.11, P(E)= ?

Q: P(x=x) 0.20, 0.30, 0.20 and 0.30, respectively, which value of V(x) is the following? Please select…

A: First we will calculate the expected value or E(X).         x=2,3,4,5P(X=x)=0.20, 0.30, 0.20, 0.30…

Q: a)     If P(A) = 0.50, P(B) = 0.60 and the P(A| B)= 0.4, then find the P (A U B)                i.…

A: Given,P(A)=0.50P(B)=0.60P(A|B)=0.4

Q: Given P(E or F) = 0.72, P(F) = 0.43, and P(E and F) = 0.09, what is P(E)?

A: Given P(E or F) = 0.72, P(F) = 0.43, and P(E and F) = 0.09

Q: Suppose ℙ(?1|?2)=0.46P(E1|E2)=0.46, ℙ(?2|?1)=0.92P(E2|E1)=0.92, and ℙ(?1)×ℙ(?2)=P(E1)×P(E2)=0.24.…

A: * SOLUTION :-  From the given information the calculation is given as follows

Q: P(A U B) = 0.9, P(B) = 0.8, P(A n B) = 0.5. Find P(A). %D

A: We have given that,  P(A∪B) = 0.9, P(B) = 0.8 and P(A∩ B) = 0.5 Then,  We will find P(A) = ?

Q: Given P(E or F) = 0.71, P(F) = 0.12, and P(E and F) = 0.18, what is P(E)?

A: The given problem is to find the value of P(E) with the given P(E or F)=0.71, P(F)=0.12, P(E and…

Q: Given P(E or F) = 0.82, P(F) = 0.25, and P(E and F) = 0.14, what is P(E)?

A:

Q: Given that p(A)=.55, p(B)=.35, and p(A| B)=.85, find p(A and B).

A: Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: Given P(E or F) = 0.78, P(E) = 0.10, and P(E and F) = 0.18, what is P(F)?

A: Given that P(E or F) = 0.78, P(E) = 0.10, and P(E and F)=0.18

Q: Given P(E or F) = 0.12, P(E) = 0.22, and P(F) = 0.18, what is P(E and F)?

A:

Q: If P(A) = 0.7, P(B) = 0.4 and P(A/B) = 0.28, then P(B/A) is %3D %3D Select one: a. 0.16 O b.0.48 c.…

A:

Q: Let P (A) = 0.4 and P (A ∪ B) = 0.6. For what value of P (B) are A and B independent?

A:

Q: Given P(A) = 0.20, P(B) = 0.25, and P(B|A) = 0.25, are A and B independent or dependent?

A: PA=0.20, PB=0.25 and PB|A=0.25

Q: if  Let P(C) = 0.2, Let P(D) = 0.3, Let P(C | D) = 0.4  how do you find P(D | C)

A:

Q: Given P(E) = 0.21, P(F) = 0.13, and P(E and F) = 0.10, what is P(E or F)?

A: I have appended the formula used in the solution procedure

Q: Given P(E) = 0.26, P(F) = 0.48, and P(E and F) = 0.11, what is P(E or F)?

A:

Q: Given P(E) = 0.23, P(F) = 0.34, and P(E and F) = 0.08, what is P(E or F)

A: P(E) = 0.23, P(F) = 0.34, and P(E and F) = 0.08.

Q: Given that p(A)=.31, p(B│A) =.39, and p(A│B) =.31, are A and B (a) independent? (b) exclusive?

A: given data  P(A) = 0.31 P(A|B) = 0.31 P(B|A) = 0.39

Q: Given P(E or F) = 0.04, P(E) = 0.35, and P(F) = 0.26, what is P(E and F)?

A: Given Information P(E or F) = 0.04 P(E) = 0.35 P(F) = 0.26 P(E and F)

Q: Given P(A) = 0.22, P(B) = 0.24, and P(B|A) = 0.21, are A and B independent or dependent?

A: We know,  P(B/A) = P(A∩B)/P(A)     P(A∩B) = P(A) P(B) Events A and B are independent if the equation…

Q: iven P(A) = 0.25, P(B) = 0.28, and P(B|A) = 0.28, are A and B independent or dependent?

A:

Q: Given P(E or F)=0.87, P(E)=0.14, and P(E and F)=0.19, what is P(F)?

A: We have given that,  P(E or F) = 0.87, P(E) = 0.14                              and P(E and F)= 0.19…

Addition Rule of Probability

It simply refers to the likelihood of an event taking place whenever the occurrence of an event is uncertain. The probability of a single event can be calculated by dividing the number of successful trials of that event by the total number of trials.

Expected Value

When a large number of trials are performed for any random variable ‘X’, the predicted result is most likely the mean of all the outcomes for the random variable and it is known as expected value also known as expectation. The expected value, also known as the expectation, is denoted by: E(X).

Probability Distributions

Understanding probability is necessary to know the probability distributions. In statistics, probability is how the uncertainty of an event is measured. This event can be anything. The most common examples include tossing a coin, rolling a die, or choosing a card. Each of these events has multiple possibilities. Every such possibility is measured with the help of probability. To be more precise, the probability is used for calculating the occurrence of events that may or may not happen. Probability does not give sure results. Unless the probability of any event is 1, the different outcomes may or may not happen in real life, regardless of how less or how more their probability is.

Basic Probability

The simple definition of probability it is a chance of the occurrence of an event. It is defined in numerical form and the probability value is between 0 to 1. The probability value 0 indicates that there is no chance of that event occurring and the probability value 1 indicates that the event will occur. Sum of the probability value must be 1. The probability value is never a negative number. If it happens, then recheck the calculation.