**Problem 14: Calculating Joint Probability**Suppose that the probability that Bob will go downtown is 45%. Now, also suppose that if Bob goes downtown, the probability that he will stop by a coffee shop is 68%. Find the probability that Bob will go downtown and stop at a coffee shop.**Options:**A. 0.306 B. 0.326 C. 0.346 D. 0.366 To solve the problem, use the formula for joint probability:\[ P(A \text{ and } B) = P(A) \times P(B|A) \]Where:- \( P(A) \) is the probability that Bob goes downtown.- \( P(B|A) \) is the probability that Bob stops at a coffee shop given that he goes downtown.Substitute the given probabilities:\[ P(A \text{ and } B) = 0.45 \times 0.68 = 0.306 \]Thus, the probability that Bob will go downtown and stop at a coffee shop is **0.306**. The correct answer is **A**.

Answer - The probability that Bob will go downtown is 45% = 0.45 The probability that he will stop by a coffee shop is 68% = 0.68Now, The probability that Bob will go downtown and stop at a coffee shop is = 0.45*0.68 = 0.306 So Option (A) is correct

Answered: 14. Suppose that the probability that…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

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Problem 1P

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14. Suppose that the probability that Bob will go downtown is 45%. Now, also suppose that if Bob goes downtown, then the probability that he will stop by a coffee shop is 68%. Find the probability that Bob will go downtown and stop at a coffee shop. A. 0.306 B. 0.326 C. 0.346 D. 0.366