Question

There are two boxes A and B. Box A has three red and four blue balls. Box B has five red and two blue balls. Anya draws a ball from each bag randomly. What is the probability that both balls are red

Answer 1

red ball from box A = 3
red ball from box B = 5

red from A and B = 3/7 * 5/7 = 15/49

Answer 2

Given,

Red balls in box A = 3

Blue balls in box A = 4

Red balls in box B = 5

Blue balls in box B = 2

To Find,

The probability that both balls are red =?

Solution,

We can solve the question as follows:

First, we will find the probability of drawing a red ball from each box.

Let, E be an event and S be the sample space. Then the probability of E is:

$P(E) = \frac{n(E)}{n(S)}$

$n(E) =$ Number of favourable outcomes

$n(S) =$ Total number of outcomes

Now, in box A,

Total balls = 7

Red balls = 3

Probability of drawing a red ball from box A$= \frac{3}{7}$

In box B,

Total balls = 5

Red balls = 7

Probability of drawing a red ball from box B$= \frac{5}{7}$

Now, the probability that both balls are red = $\frac{3}{7} *\frac{5}{7}$

                                                                        $= \frac{15}{49}$

Hence, the probability that both balls are red is 15/49.