Question

A basket contains 10 ripe and 4 unripe bananas. If three bananas are taken from the basket one after the other, determine the possible values of the random variable U representing the number of unripe bananas

Answer 1

Let $R$ represent the ripe bananas and let $U$ represent the unripe bananas.

List the sample space of this experiment

$$S=\{RRR, RRU, RUR, URR,$$

$$RUU, URU, UUR, UUU\}$$

The values of random variable $U$ are $0, 1, 2, 3.$

There are 8 possible outcomes:

one with $U=0\ (RRR),$

three with $U=1\ (RRU, RUR, URR),$

three with $U=2\ (RUU, URU, UUR),$

one with $U=3\ (UUU).$

Then

$$P(U=0)=\dfrac{1}{8}$$

$$P(U=1)=\dfrac{3}{8}$$

$$P(U=2)=\dfrac{3}{8}$$

$$P(U=3)=\dfrac{1}{8}$$

Construct the probability distribution of random variable $U$

$$\begin{matrix} u & 0 & 1 & 2 & 3 \\ p(u) & 1/8 & 3/8 & 3/8 & 1/8 \end{matrix}$$