JEE Advanced 2013 · Paper 2 · Mathematics Q51

← JEE Advanced 2013 · Paper 2

MathematicsSingle correct+3 / -1Question 51 of 60

Passage

Paragraph for Questions 51 and 52

A box $B_1$ contains 1 white ball, 3 red balls and 2 black balls. Another box $B_2$ contains 2 white balls, 3 red balls and 4 black balls. A third box $B_3$ contains 3 white balls, 4 red balls and 5 black balls.

If 1 ball is drawn from each of the boxes $B_1$ , $B_2$ and $B_3$ , the probability that all 3 drawn balls are of the same colour is

\dfrac{82}{648}

\dfrac{90}{648}

\dfrac{558}{648}

\dfrac{566}{648}

Answer and worked solution

Official answer: A

Same colour from $B_1$ (1W 3R 2B), $B_2$ (2W 3R 4B), $B_3$ (3W 4R 5B):

white: $\frac16\cdot\frac29\cdot\frac3{12}=\frac6{648}$
red: $\frac36\cdot\frac39\cdot\frac4{12}=\frac{36}{648}$
black: $\frac26\cdot\frac49\cdot\frac5{12}=\frac{40}{648}$

Total $\dfrac{82}{648}$ .

(A)

Topics:Independent events

← Previous question Next question →

JEE Advanced 2013 · Paper 2, Mathematics question 51