Question

A bag contains 4 blue balls and 6 red balls. A magician draws a ball at random from the bag, notes its colour and then replaces it. He repeats this procedure an additional 5 more times (so that he makes a total of 6 random draws with replacement). What is the probability that out of the 6 balls drawn, 2 of them are red?

Answer 1

$\fontsize{18}{10}{\textup{\textbf{The required probability is 0.02.}}}$

Step-by-step explanation:  

Number of blue balls = 4  and  number of red balls = 6.

The magician draws 6 balls from the bag with replacement.

So, for 2 of the drawn balls to be red, the other 4 must be blue.

Now,

the number of ways in which 2 red balls and 4 blue balls are drawn out of 4 blue balls and 6 red balls is

$n=4\times 4\times 6\times6\times6\times6=4^2\times6^4.$

And, the number of ways in which 6 balls can be drawn from 10 balls with replacement is

$N=10\times10\times10\times10\times10\times10=10^6.$

Therefore, the probability that out of the 6 balls drawn, 2 of them are red is

$p=\dfrac{n}{N}=\dfrac{4^2\times6^4}{10^6}=\dfrac{20736}{1000000}=0.02.$

Thus, the required probability is 0.02.