Question

The probability that an event does not happen in one trial is $0.8$. The probability that the event happens atmost once in three trials is

• A. $0.896$
• B. $0.791$
• C. $0.642$
• D. $0.592$

Answer 1

The correct option is A $0.896$

$p=0.2,q=0.8,n=3$
Atmost one success means either $0success$ or $1success$. So, either it is $3failures$ or $2failures$.
Hence, Probability of atmost one success is $=P\left(3failures\right)+P\left(2failures\right)$
using binomial probability distribution formula
${=}^3{C}_0\times {0.8}^3{+}^3{C}_1\times {0.8}^2\times 0.2=.512+.384=.896$