JEE Main · 2023 · 30 Jan 2023 · Shift 1 · Probability

If an unbiased die, marked with

- 2, - 1, 0, 1, 2, 3

on its faces, is thrown five times, then the probability that the product of the outcomes is positive, is:

Answer: (B)

Solution

The faces give a positive outcome

{1, 2, 3}

with probability

\frac{1}{2}

, a negative outcome

{- 2, - 1}

with probability

\frac{1}{3}

, and zero with probability

\frac{1}{6}

. The product of five throws is positive exactly when no zero occurs and the number of negatives is even, i.e.

0

2

4

negatives:

P = (0 5) (\frac{1}{2})^{5} + (2 5) (\frac{1}{3})^{2} (\frac{1}{2})^{3} + (4 5) (\frac{1}{3})^{4} (\frac{1}{2}) .

Evaluating,

\frac{1}{32} + \frac{10}{72} + \frac{5}{162} = \frac{81 + 360 + 80}{2592} = \frac{521}{2592} .

JEE Main · 2023 · 30 Jan 2023 · Shift 1 · Single correct option