Question

11 black balls and 14 white balls are placed in an urn. two balls are then drawn in succession. what is the probability that the second ball drawn is a white ball if the second ball is drawn without replacing the first ball?

Answer 1

$|\Omega|=25\cdot24=600\\ |A|=11\cdot14+14\cdot13=154+182=336\\\\ P(A)=\dfrac{336}{600}=\dfrac{14}{25}=56\%$

Answer 2

The probability that the second ball drawn is a white ball if the second ball is drawn without replacing the first ball is;

P(second ball being white) = 42/75

We are told there are;

Number of black balls = 11

Number of white balls = 14

Total number of balls = 25 balls

Since 2 balls are drawn without replacement, then;

possible number of ways of drawing the two balls = 25 × 24 = 600

Now, to find the probability of drawing two white balls;

Probability the first ball being white and second white = (14/25 × 13/24) = 91/300

Probability of the first ball being black and the second being white = (11/25 × 14/24) = 77/300

Thus;

P(second ball being white) = (91/300) + (77/300)

P(second ball being white) = 168/300 = 42/75

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