Question

A man either drives a car or catches a train to go to his office every day.

His traveling habits are as follows: “He never goes 2 days in a row by

train. But if he drives one day, then the next day he is likely (equally) to

travel by train as he is drive again”. On the first day of the week he

throws a die and drive to his office if and only if a 6 appears. Find the

probability that

(i) He goes by train to his office on the third of week.​

Answer 1

Answer:

11/24

Step-by-step explanation:

Answer 2

Given,

A man either drives a car or catches a train

He never goes 2 days in a row by train

But if he drives one day, then the next day he is likely (equally) to travel by train as he is driving again

On the first day of the week, he throws a die and drives to his office if and only if a 6 appears

To Find,

The probability that he goes by train to his office on a third of the week=?

Solution,

The probability of going by train = 1/2

The probability of going by car = 1/2

The probability of going by car on the first day = 1/6 [Probability of getting 6 on die]

The probability of going by train on the first day = 1 - 1/6 = 5/6

The probability distribution on the  first day = (5/6, 1/6)

The probability distribution on the second day = (5/6, 1/6)(0, 1)(1/2,1/2)

The probability distribution on the second day = (1/11,11/12)

The probability distribution on the third day = (1/11,11/12)(0,1)(1/2,1/2)

The probability distribution on the third day = (11/24,13/24)

Hence, the probability that he goes by train to his office on the third of the week is 11/24