Question

Suppose 40 % of students who drive to campus carry jump cables in their cars in case of a dead battery emergency. Suppose further your car battery dies and that you do not have jumper cables in your car. Consider the experiment of stopping other students and asking to borrow jumper cables so that you are able to "jump" or re-energize your car battery.

Accordingly, let X ="number of students who must be stopped before find a student with jumper cables."

i) Give the probability mass function for this random variable, i.e. PX(X = x)
ii) Compute the probability PX(X = 1).

Answer 1

The probability mass function (PMF) for the random variable X, which represents the number of students who must be stopped before finding a student with jumper cables, can be defined as P(X = x) = (0.6^(x-1))(0.4). The probability of X equaling 1 is 0.4.

Step-by-step explanation:

i) Probability mass function (PMF) for random variable X:

The probability mass function (PMF) describes the probability of each possible value of a discrete random variable. In this case, the random variable X represents the number of students who must be stopped before finding a student with jumper cables.

Since each student has a 40% chance of carrying jumper cables, we can define the PMF as:

P(X = x) = (0.6^(x-1))(0.4), where x is the number of students stopped before finding one with jumper cables.

ii) Probability P(X = 1):

To compute the probability that X equals 1, we substitute x = 1 into the PMF:

P(X = 1) = (0.6^(1-1))(0.4) = 0.4