Suppose that the probability for a student to get a free lift to a university on

Question

Suppose that the probability for a student to get a free lift to a university on any morning is 0.4. The student needs to get a taxi if she/he does not get a lift and she/he needs to pay 20 QAR for a Taxi..

Determine the probability that in a week (five days), the student will get a lift only twice?

Determine the probability that the student will get his/her first lift on the third day?

Suppose a given month with 15 days. What is expectation of the amount of money that the student needs to pay in a month.

Explanation / Answer

A)Let X be the number of days in a week that the student will get a lift. Then X hasa Binomial distribution with

n = 5 and P=0.4

2=( X=P) 5C2 *0.4^2 * 0.6 ^3

=( 5! / 2!×3! )0.16×0.216 = 0.345

B) Since in this part, we are dealing with the first lift, then we need to usegeometric distribution.

Let Y denote the number of days until the first lift

0.6=.(3= Y) P^2×0.4 = 0.144

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