a. Tommy drives to work every morning. There are two routes for him to choose fr

Question

a. Tommy drives to work every morning. There are two routes for him to choose from. The probability of choosing route A is twice that of route B. Suppose the probabilities that there will be traffic congestion on route A and route B are and , respectively. i. Find the probability that Tommy will come across traffic congestion on a given ii. On two successive days, find the probability that Tommy comes across traffic morning congestion on at least one of the two days. If Tommy comes across traffic congestion on a particular morning, find the probability that he drove to work that day via route A. iii.

Explanation / Answer

Here we are given that P(A) = 2P(B)

Now, we know that P(A) + P(B) = 1

Therefore 3P(B) = 1

P(B) = 1/ 3 and P(A) = 2/ 3

Also, we are given here that:

P( traffic | A) = 1/6 and P( traffic | B) = 4/9

a) Now using law of total probability, we get:

P( traffic ) = P( traffic | A)P(A) + P( traffic | B) P(B) = (1/6)*(2/3) + (4/9)*(1/3) = 0.2593

Therefore 0.2593 is the required probability here.

b) On 2 consecutive days probability that he gets traffic at least one day is computed as:

= 1 - Probability that he does not get traffic in either of the two days

= 1 - (1 - 0.2593)2

= 0.4513

Therefore 0.4513 is the required probability here.

c) Using bayes theorem, we get here:

P(A | traffic ) = P( traffic | A)P(A) / P( traffic ) = (1/6)*(2/3) / 0.2593 = 0.1111/ 0.2593 = 0.4285

Therefore 0.4285 is the required probability here.

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.