Question

A bag contains three red balls and two blue balls. We remove successively, and with replacement, two balls and observe their colour. What is the probability of "to extract a red ball and a blue one, without taking into account the order"?

• A. $\frac{12}{25}$
• B. $\frac{13}{25}$
• C. $\frac{12}{23}$
• D. None of these

Answer 1

The correct option is A $\frac{12}{25}$

Given:

Total number of balls in a bag = 3 red balls + 2 blue balls = 5

Let's consider the events: R= "to remove a red ball", A=R'= "to remove a blue ball.

Our sample space is: (RR, RA, AR, AA}, and the events that we are interested in are RA and AR.

We represent our problem in a tree as shown in the figure

Using the law of total probability,

$P\left(S\right)=P\left(R\right)\times P\left(A/R\right)+P\left(A\right)\times P\left(R/A\right)=\frac{3}{5}\times \frac{2}{5}+\frac{2}{5}\times \frac{3}{5}=\frac{12}{25}$

is the required probability.