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A box contains 10 black and 10 white balls. What is the probability of drawing 2 balls of the same colour ?
Answer & Solution
Correct Answer:
Option
A
Total number of balls = (10 + 10) = 20
Let E be the event of drawing 2 balls of the same colour.
n (E) = number of ways of drawing 2 black balls or 2 white balls.
n (E) = $$\left( {{}^{10}\mathop C\nolimits_2 \times {}^{10}\mathop C\nolimits_2 } \right)$$ $$ = 2 \times {}^{10}\mathop C\nolimits_2 $$ $$ = 2 \times \frac{{10 \times 9}}{{2 \times 1}}$$ = 90
n (S) = number of ways of drawing 2 balls out of 20 balls
$$ = {}^{20}\mathop C\nolimits_2 = \frac{{20 \times 19}}{{2 \times 1}}$$ = 190
$$\therefore P(E) = \frac{{n(E)}}{{n(S)}} = \frac{{90}}{{190}} = \frac{9}{{19}}$$
Let E be the event of drawing 2 balls of the same colour.
n (E) = number of ways of drawing 2 black balls or 2 white balls.
n (E) = $$\left( {{}^{10}\mathop C\nolimits_2 \times {}^{10}\mathop C\nolimits_2 } \right)$$ $$ = 2 \times {}^{10}\mathop C\nolimits_2 $$ $$ = 2 \times \frac{{10 \times 9}}{{2 \times 1}}$$ = 90
n (S) = number of ways of drawing 2 balls out of 20 balls
$$ = {}^{20}\mathop C\nolimits_2 = \frac{{20 \times 19}}{{2 \times 1}}$$ = 190
$$\therefore P(E) = \frac{{n(E)}}{{n(S)}} = \frac{{90}}{{190}} = \frac{9}{{19}}$$
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LoginWhite balls=10
Total balls=20
Probability of 2/both same colour balls=10C2+10C2/20C2=9/19