Search any question & find its solution
Question:
Answered & Verified by Expert
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
Options:
Solution:
2395 Upvotes
Verified Answer
The correct answer is:
$0.896$
Given, $p=0.2, q=0.8, n=3$
From binomial distribution,
$P(X=r)={ }^n C_2 P^r q^{n-r}$
Probability that event happens at most once,
$P(X \leq 1)=P(X=0)+P(X=1)$
$\begin{aligned} & ={ }^3 C_0(0.2)^0(0.8)^{3-0}+{ }^3 C_1(0.2)^1(0.8)^{3-1} \\ & =\frac{3 !}{0 ! 3 !} \times 1 \times\left(\frac{8}{10}\right)^3+\frac{3 !}{1 ! 2 !}\left(\frac{2}{10}\right)\left(\frac{8}{10}\right)^2 \\ & =\frac{64}{125}+\frac{48}{125}=\frac{112}{115}=0.896\end{aligned}$
From binomial distribution,
$P(X=r)={ }^n C_2 P^r q^{n-r}$
Probability that event happens at most once,
$P(X \leq 1)=P(X=0)+P(X=1)$
$\begin{aligned} & ={ }^3 C_0(0.2)^0(0.8)^{3-0}+{ }^3 C_1(0.2)^1(0.8)^{3-1} \\ & =\frac{3 !}{0 ! 3 !} \times 1 \times\left(\frac{8}{10}\right)^3+\frac{3 !}{1 ! 2 !}\left(\frac{2}{10}\right)\left(\frac{8}{10}\right)^2 \\ & =\frac{64}{125}+\frac{48}{125}=\frac{112}{115}=0.896\end{aligned}$
Looking for more such questions to practice?
Download the MARKS App - The ultimate prep app for IIT JEE & NEET with chapter-wise PYQs, revision notes, formula sheets, custom tests & much more.