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Chapter 5: Q. 105. (page 337)

Suppose a loaded die has the following probability model:

If this die is thrown and the top face shows an odd number, what is the probability that the die shows a 1?

a. 0.10

b. 0.17

c. 0.30

d. 0.50

e. 0.60

Short Answer

Expert verified

The probability that the die shows a1is0.60

Step by step solution

01

Given information

Probability model for loaded die:

02

Calculation

The addition rule for disjoint or mutually exclusive events is as follows:

P(A∪B)=P(AorB)=P(A)+P(B)

Definition of conditional probability:

P(B∣A)=P(A∩B)P(A)=P(AandB)P(A)

From the table,

Probability to roll a 1

P(1)=0.3

When it comes to the chances of rolling an odd number(1,3or5)

For disjoint events, use the following addition rule:

P(odd)=P(1)+P(3)+P(5)=0.3+0.1+0.1=0.5

Definition of conditional probability:

P(1∣odd)=P(l andodd)P(odd)=0.30.5=35=0.60

Therefore, the conditional probability to roll 1 is0.60

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