Search any question & find its solution
Question:
Answered & Verified by Expert
The probability that a ship safely reaches a port is $\frac{1}{3}$. The probability that out of 5 ships, at least 4 ships would arrive safely is
Options:
Solution:
2201 Upvotes
Verified Answer
The correct answer is:
$\frac{11}{243}$
Probability that a ship reaches port $=\frac{1}{3}$
Probability that a ship not reaching port $=1-\frac{1}{3}=\frac{2}{3}$ Number of ships $(\mathrm{n})=5$. $\mathrm{r}=4,5$
$\mathrm{p}(4)+\mathrm{p}(5)={ }^{5} \mathrm{c}_{4}\left(\frac{1}{3}\right)^{4}\left(\frac{2}{3}\right)^{5-4}+{ }^{5} \mathrm{c}_{5}\left(\frac{1}{3}\right)^{5}\left(\frac{2}{3}\right)^{5-5}$
$=5\left(\frac{2}{3^{5}}\right)+\frac{1}{3^{5}}$
$=\frac{10}{243}+\frac{1}{243}=\frac{11}{243}$
Probability that a ship not reaching port $=1-\frac{1}{3}=\frac{2}{3}$ Number of ships $(\mathrm{n})=5$. $\mathrm{r}=4,5$
$\mathrm{p}(4)+\mathrm{p}(5)={ }^{5} \mathrm{c}_{4}\left(\frac{1}{3}\right)^{4}\left(\frac{2}{3}\right)^{5-4}+{ }^{5} \mathrm{c}_{5}\left(\frac{1}{3}\right)^{5}\left(\frac{2}{3}\right)^{5-5}$
$=5\left(\frac{2}{3^{5}}\right)+\frac{1}{3^{5}}$
$=\frac{10}{243}+\frac{1}{243}=\frac{11}{243}$
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.