Mathematics · Probability

JEE Main 2024 — 31 January, Shift 2 — Question 18

A coin is based so that a head is twice as likely to occur as a tail. If the coin is tossed 3 times, then the probability of getting two tails and one head is-

Option A:
$\frac{2}{9}$
Correct
Option B:
$\frac{1}{9}$
Option C:
$\frac{2}{27}$
Option D:
$\frac{1}{27}$

Answer: A

Step-by-step solution

Let probability of tail is $\frac{1}{3}$

$\Rightarrow$ Probability of getting head $=\frac{2}{3}$

$\therefore$ Probability of getting 2 tails and 1 head

$=\left(\frac{1}{3} \times \frac{2}{3} \times \frac{1}{3}\right) \times 3$

$=\frac{2}{27} \times 3$

$=\frac{2}{9}$

Answer key and solution verified before publishing.

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Exam: JEE Main 2024
Paper: 31 January, Shift 2
Subject: Mathematics
Chapter: Probability
Topic: Independent Events

Let the mean and the variance of 6 observation a, b, 68,44,48,60 be 55 and 194 , respectively if a b , then a+3 b is

Answer: A

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