Question

. A bag contains 8 white and 6 red balls. Find
the probability of drawing two balls of the
same colour.
(A) 15/91
(B) 43/91
(C) 51/91
(D) 28/91​

Answer 1

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Step-by-step explanation:

Answer 2

The probability of drawing two balls of the same color are $\frac{43}{91}$

Answer:   (Option B).

Given Data:

8 white Ball

6 Red Ball

Step 1:

Let us assume the probability is 100%.

So you draw one ball. The probability that it's red is $\frac{8}{14}=\frac{4}{7}$

You draw again.  

Probability (Second red) $=\frac{7 \text { (red balls remains) }}{13(\text { balls remaining })}$

Step 2:

The probability of drawing two red balls is therefore $\frac{4}{7} \times \frac{7}{13}=\frac{4}{13}$

Now, suppose instead of a red on the first draw you got white.  

The probability of this is $\frac{6}{14}=\frac{3}{7}$

Step 3:

Given the first ball is white, the probability of drawing a second white is $\frac{5}{13}$

P (two whites) = $\frac{3}{7} \times \frac{5}{13}=\frac{15}{91}$

Step 4:

P (Two balls of same color) =  $\frac{4}{13} \times \frac{15}{91}=\frac{43}{91}$