Question

How to compute the question (b)? And why it isn't 6C2·0.3^2·0.7^4?

The probability that Jim goes to work by taxi is 0.3. He works 6 days in a week.

(a) Find the probability that Jim goes to work by taxi in at least 3 days in a week given that

(i) he goes to work by taxi for at most 4 days,

(ii) he goes to work by taxi for more than 1 day.

(b) Find the probability that Jim goes to work by taxi in exactly 2 consecutive mornings.

Answer 1

Question asked:

The probability that Jim goes to work by taxi is 0.3. He works 6 days in a week.

(b) Find the probability that Jim goes to work by taxi in exactly 2 consecutive mornings.

How to compute the question (b)? And why it isn't 6C2·0.3^2·0.7^4?

We cannot apply Binomial Distribution in this problem because the question is not " Find the probability that Jim goes to work by taxi in exactly 2 mornings" but the question is: " Find the probability that Jim goes to work by taxi in exactly 2 consecutive mornings".

So,

the correct answer to the given question is not: 6C2·0.3^2·0.7^4.

The correct answer is as follows:

Given:

Probability that Jim goes to work by taxi in one day = 0.3

Number of days Jim goes to office = 6 days.

So,

For 6 days of working, average number of days Jim goes to office by taxi = 6 X 0.3 = 1.8

So,

For going to office on 2 consecutive days:

For the first of the two consecutive days, Probability of going by taxi = 1.8/ 6 = 0.3, since total of 6 days are available.

For the second day of the two consecutive days, Probability of going by taxi = 1.8/5 = 0.36, since 1 day out of 6 days is gone for the first day.

Thus, Probability that Jim goes to office by taxi on 2 consecutive days = 0.3 X 0.36 = 0.1080

So,

Answer is:

0.1080