ISRO CS 2023 Q.44: solution and answer

ISRO 2023 · CSQ.44 · 1 mark · MCQ

If a bag contains 6 blue balls, 5 white balls and 4 yellow balls and if a ball is drawn out at random, probability of not getting a white ball is

(A)
$\frac{2}{3}$
(B)
$\frac{1}{3}$
(C)
$\frac{1}{5}$
(D)
None of the above

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Answer and solution

ANSWER

The probability of not getting a white ball is $\frac{2}{3}$ , option (A).

Official answer: ASource: ISRO's revised and final answer key of 16 February 2024

The bag holds $6 + 5 + 4 = 15$ balls, and each ball is equally likely to be drawn.
Balls that are not white are the blue and yellow ones: $6 + 4 = 10$ .
$P (not white) = \frac{10}{15} = \frac{2}{3}$
Check with the complement rule: $P (\overline{W}) = 1 - P (W) = 1 - \frac{5}{15} = 1 - \frac{1}{3} = \frac{2}{3}$ .
Option (b), $\frac{1}{3}$ , is the probability of drawing a white ball. Option (c), $\frac{1}{5}$ , matches no event here. Option (d) is wrong because (a) is correct.

KEY IDEA

With equally likely outcomes, probability is favourable count over total count. "Not white" can be counted directly (10 of 15) or found as 1 minus the probability of white.

WATCH OUT FOR

Computing the probability of drawing a white ball, $\frac{5}{15} = \frac{1}{3}$ , and picking it, which answers the opposite question.

From the ISRO CS 2023 paper. Every question of this paper · The full paper (PDF, ISRO) · All 5 ISRO Counting & axioms questions, with notes

ISRO CS 2023 Q.44: solution and answer

Answer and solution

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