Question

A meeting of envoys was attended by 4 Koreans and 2 Filipinos. If two envoys were

selected at random one after the other, determine the values of the random variable K

representing the number of Koreans. Construct the probability histogram.

Answer 1

Solution

There are 4 Koreans and 2 Filipinos.

Let;

K represent the number of Koreans

F represent the number of Filipinos

If two people are chosen at random one after the other there are 3 possible outcomes

1. Both the selected people are Filipinos and hence $K=0$
2. One Korean and one Filipino is chosen hence $K=1$
3. Both of the selected people are Koreans and hence $K=2$

The probability values of K are as follows

$K=0:~P(F,F)$

$=\dfrac26\times\dfrac15=\dfrac{1}{15}$

$K=1: ~P(K,F) or P(K,F)$

$=(\dfrac46\times\dfrac25)+(\dfrac26\times\dfrac45)=\dfrac{8}{15}$

$K=2:~P(K,K)$

$=\dfrac46\times\dfrac35=\dfrac25$

The probability histogram