Question

There are 12 balls in a bag. One is blue and one is red. What is the exact probability that the blue ball is drawn first and the red ball is drawn second? (Without replacement)

Answer 1

The exact probability that the blue ball is drawn first and the red ball is drawn second is $\frac{1}{132}$

Solution:

The probability of an event is given as:

$Probability = \frac{ \text{ number of favorable outcomes }}{ \text{ total number of possible outcomes }}$

Given that,

There are 12 balls in a bag

One is blue and one is red

Favorable outcome = blue ball is drawn first

Favorable outcome = 1

Therefore,

$Probability = \frac{1}{12}$

Now, without replacement, red ball is drawn second

Therefore,

Total possible outcomes = 12 - 1 = 11

$Probability = \frac{1}{11}$

What is the exact probability that the blue ball is drawn first and the red ball is drawn second?

$Total\ probability = \frac{1}{12} \times \frac{1}{11} = \frac{1}{132}$

Thus the exact probability that the blue ball is drawn first and the red ball is drawn second is $\frac{1}{132}$