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a.
To determine:
The probability of rolling two six-sided die and obtaining 2 and 3.
Introduction:
The six-sided die is a cube, on which the numbers from 1 to 6 are marked once. When the die is rolled one number is obtained as the outcome.
a.
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Explanation of Solution
The number 2 is written only once on the die and can be expressed once. The number of chances that two will appear on die is one. The total numbers that can appear on die are six.
The probability for obtaining two on a six-sided die is as follows:
Probability=Number of chances that 2 will appearTotal numbers that can appear on a die=16
The number 3 is written only once on the die and can be expressed once. The number of chances that three will appear on die is one. The total numbers that can appear on die are six.
The probability for obtaining three on a six-sided die is as follows:
Probability=Number of chances that 3 will appearTotal numbers that can appear on a die=16
The probability of obtaining two or three can be calculated using the product rule that is by multiplying individual probabilities of each number. The probability of obtaining two or three is as follows:
(P)of obtaining two or three=(P) of obtaining two×(P) of obtaining three=16×16=136
b.
To determine:
The probability of rolling two six-sided die and obtaining 6 and 6.
Introduction:
The six-sided die is a cube, on which the numbers from 1 to 6 are marked once. When the die is rolled one number is obtained as the outcome.
b.
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Explanation of Solution
The number 6 is written only once on the die and can be expressed once. The number of chances that six will appear on die is one. The total numbers that can appear on die are six.
The probability for obtaining six on a six-sided die is as follows:
Probability=Number of chances that 6 will appearTotal numbers that can appear on a die=16
The probability of obtaining six or six can be calculated using the product rule that is by multiplying individual probabilities of each number. The probability of obtaining six or six is as follows:
(P)of obtaining six or six=(P) of obtaining six×(P) of obtaining six=16×16=136
c.
To determine:
The probability of rolling two six-sided die and obtaining at least one 6.
Introduction:
The six-sided die is a cube, on which the numbers from 1 to 6 are marked once. When the die is rolled one number is obtained as the outcome.
c.
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Explanation of Solution
The number 6 is written only once on the die and can be expressed once. The number of chances that six will appear on die is one. The total numbers that can appear on die are six.
The probability for obtaining six on a six-sided die is as follows:
Probability=Number of chances that 6 will appearTotal numbers that can appear on a die=16
The probability of obtaining any number but a six is as follows:
Probability=Number of chances that 6 will not appearTotal numbers that can appear on a die=56
The probability of obtaining at least one six on rolling two six-sided die is as follows:
(P)of obtaining at least one six=((P) of obtaining six on a first die+[((P)) of obtaining any number but six×(P) of obtaining six on a second die])=16+56×16=6+536=1136
d.
To determine:
The probability of rolling two six-sided die and obtaining two of the same number (two 1 s, or two 2s, or two 3s, etc.).
Introduction:
The six-sided die is a cube, on which the numbers from 1 to 6 are marked once. When the die is rolled one number is obtained as the outcome.
d.
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Explanation of Solution
The number 1 is written only once on the die and can be expressed once. The number of chances that one will appear on die is one. The total numbers that can appear on die are six.
The probability for obtaining one on a six-sided die is as follows:
Probability=Number of chances that 1 will appearTotal numbers that can appear on a die=16
The probability of obtaining one or one can be calculated using the product rule that is by multiplying individual probabilities of each number. The probability of obtaining one or one is as follows:
(P)of obtaining one or one=(P) of obtaining one×(P) of obtaining one=16×16=136
Similarly, the probability of obtaining two or two will be 136 and so on.
The probability of obtaining two 1s, two 2s, two 3s, two 4s, two 5s, and two 6s is as follows:
Probability=(Probability of obtaining two 1s +Probabilty of obtaining two 2s +Probabilty of obtaining two 3s +Probabilty of obtaining two 4s +Probabilty of obtaining two 5s +Probabilty of obtaining two 6s +)
Probability=136+136+136+136+136+136=1+1+1+1+1+136=636=16
e.
To determine:
The probability of rolling two six-sided die and obtaining an even number on both dice.
Introduction:
The six-sided die is a cube, on which the numbers from 1 to 6 are marked once. When the die is rolled one number is obtained as the outcome.
e.
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Explanation of Solution
A die has three even numbers. The probability of obtaining an even number is as follows:
Probability=Number of chances that an even will appearTotal numbers that can appear on a die=36
The probability of obtaining an even number on both die can be calculated using the product rule that is by multiplying individual probabilities of each number. The probability of obtaining an even number is as follows:
(P)=(P) of obtaining an even number×(P) of obtaining an even number=36×36=936=14
f.
To determine:
The probability of rolling two six-sided die and obtaining an even number on at least one die.
Introduction:
The six-sided die is a cube, on which the numbers from 1 to 6 are marked once. When the die is rolled one number is obtained as the outcome.
f.
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Explanation of Solution
A die has three even numbers. The probability of obtaining an even number is as follows:
Probability=Number of chances that an even will appearTotal numbers that can appear on a die=36
A die has three even numbers. The probability of not obtaining an even number is as follows:
Probability=Number of chances that an even will not appearTotal numbers that can appear on a die=36
An even number can be an outcome on first die but not on second die.
The probability of obtaining an even number on first die and not obtaining on second die can be calculated using the product rule that is by multiplying individual probabilities of each number. The probability of obtaining an even number on first die and not obtaining on second die is as follows:
(P)=((P) of obtaining an even number on first die×(P) of not obtaining an even number on second die)=36×36=936
An even number cannot be an outcome on first die but can be on second die.
The probability of obtaining an even number on second die and not obtaining on first die can be calculated using the product rule that is by multiplying individual probabilities of each number. The probability of obtaining an even number on second die and not obtaining on first die is as follows:
(P)=((P) of obtaining an even number on second die×(P) of not obtaining an even number on first die)=36×36=936
An even number can be an outcome on both die.
The probability of obtaining an even number on both die can be calculated using the product rule that is by multiplying individual probabilities of each number. The probability of obtaining an even number on both die is as follows:
(P)=((P) of obtaining an even number on first die×(P) of not obtaining an even number on second die)=36×36=936
The probability of obtaining an even number on at least one die is as follows:
Probability=(Probability of obtaining an even number on first die but not on a second die +Probability of obtaining an even number on second die but not on a first die +Probability of obtaining an even number on both die)
Probability=936+936+936=9+9+936=2736=34
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Chapter 3 Solutions
Genetics: A Conceptual Approach
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