Question

An urn contains 11 white balls and 5 black balls.
A simple random sample with replacement (wr) of size: n = 2
is drawn from the urn.
Calculate the probability that the sample contains one ball of each color.

at least four decimal places.

Answer 1

total number of balls = 11 + 5 = 16

We will use combination to find the required probability.We have to select a sample of 2 balls, i.e. one ball of each color

total number of ways of selecting 2 balls out of 16 balls =

where n = 16 and r = 2

so, total number of ways of selecting 2 balls out of 16 balls =

16! is expressed as 16*15*14!

so, we get

total number of ways of selecting 2 balls out of 16 balls = 120

We have 11 white balls and 5 black balls, so we will find the number of ways of selecting 1 white ball and 1 black ball

We can select 1 white ball out of 11 balls in 11 different ways and we can select 1 black ball out of 5 balls in 5 different ways

So, total number of ways of selecting 1 black ball and 1 white ball = 11+5 = 16

So, Required probability = (number of ways of selecting 1 each ball)/(total number of ways selecting 2 out of 16)

setting the given values, we get

Required probability = (16/120) = 0.1333 (rounded to 4 decimals)