Question

The probability that an event $A$ occurs in a single trial of an experiment is $0.6$. Three independent trials of the experiment are performed. The probability that the event $A$ occurs at least twice is

• A. $0.636$
• B. $0.632$
• C. $0.648$
• D. $0.946$

Answer 1

Answer: (C)

$0.648$

Given , number of independent trials $n=3$
Let X be number of times event A occurs.
Probability that event A occurs in single trial $p=0.6$
$\Rightarrow q=1-0.6=0.4$
Required probability $=P(X\ge 2)$
$=P(X=2)+P(X=3)$
${=}^3{C}_2\left(0.6{)}^2\right(0.4\left){+}^3{C}_3\right(0.6{)}^3$
$=0.432+0.216=0.648$