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Chapter 10: Q. 2 (page 667)

The probability that Color Me Dandy wins a horse race at Batavia Downs given good track conditions is 0.60. The probability of good track conditions on any given day is 0.85. What is the probability that Color Me Dandy wins or the track conditions are good?

(a)0.94

(b)0.51

(c)0.49

(d) 0.06

(e) The answer cannot be determined from the given information.

Short Answer

Expert verified

The probability that Color Me Dandy wins or the track conditions are good is:

(e) The answer cannot be determined from the given information.

Step by step solution

01

Definition

General multiplication rule:

P(AandB)=P(A鈭�B)=P(A)脳P(B鈭�A)=P(B)脳P(A鈭�B)

General addition rule for any two events:

P(AorB)=P(A)+P(B)-P(AandB)

02

Explanation

P(ColorMeDandywins鈭�Goodtrack)=0.60

P(Goodtrack)=0.85

By the general multiplication rule, we can then determine P (Color Me Dandy wins and Good track) (which is the product of P( Color Me Dandy wins \mid Good track ) and P( Good track ).

However, we note that using the general addition rule, we need P(Color Me Dandy wins) to determine P(Color Me Dandy wins or Good track), and so we can't predict the answer from the given data because we don't know the probability P. (Color Me Dandy wins)..

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