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 R representing the number of ripe bananas Identify the all possible outcomes b. Count the number of ripe bananas in each outcome Construct the probability distribution of the random variable R​

Answer 1

Answer:

sample space={RRR,RRU,RUR,URR,UUR,URU,RUU,UUU}

Number of ripe in each outcome is given by-

frequency distribution of the values of the random variable R is-

probability distribution of the random variable R is-

probability histogram

Answer 2

Answer:

a.) The possible outcomes are:

    UUU, UUR, URU, RUU, URR, RUR, RRU, RRR

b.) There are 3 ripe bananas in RRR,

                      2 in URR, RUR, RRU,

                      1 in UUR, URU, RUU and

                      0 in UUU.

c.) The probability Distribution of R is :

R        0              1                  2              3

P(R)    $\frac{1}{8}$               $\frac{3}{8}$                  $\frac{3}{8}$               $\frac{1}{8}$  

Step-by-step explanation:

Given:

Number of ripe bananas = 10

Number of unripe bananas = 4

Number of bananas taken out = 3

a). Let R represent ripe bananas and U represent unripe bananas.

=> All possible outcomes = UUU, UUR, URU, RUU, URR, RUR, RRU, RRR

Therefore, the possible outcomes are:

UUU, UUR, URU, RUU, URR, RUR, RRU, RRR

b.) The number of ripe bananas in each outcome:

UUU = 0

UUR = 1

URU = 1

RUU = 1

URR = 2

RUR = 2

RRU = 2

RRR = 3

Therefore, there are 3 ripe bananas in RRR,

2 in URR, RUR, RRU,

1 in UUR, URU, RUU and

0 in UUU.

c.) We know that probability of taking out 0 ripe banana is  $\frac{1}{8}$

                            Probability of taking out 1 ripe banana is   $\frac{3}{8}$

                            Probability of taking out 2 ripe banana is   $\frac{3}{8}$

                            Probability of taking out 3 ripe banana is   $\frac{1}{8}$  

Therefore, the probability Distribution of R is :

R        0              1                  2              3

P(R)    $\frac{1}{8}$               $\frac{3}{8}$                  $\frac{3}{8}$               $\frac{1}{8}$