Question

In an examination, the probability of a candidate solving a question is $\frac{1}{2}$. Out of given $5$ questions in the examination, what is the probability that the candidate was able to solve at least $2$ questions?

• A. $\frac{1}{64}$
• B. $\frac{3}{16}$
• C. $\frac{1}{2}$
• D. $\frac{13}{16}$

Answer 1

The correct option is D $\frac{13}{16}$

Probability that the candidate was able to solve at least $2$ questions,

$P=$ Probability that the candidate solves 2 questions$+$Probability that the candidate solves 3 questions$+$Probability that the candidate solves 4 questions$+$ Probability that the candidate solves 5 questions

${=}_2^{5}C{\left(\frac{1}{2}\right)}^2{\left(\frac{1}{2}\right)}^3{+}_3^{5}C{\left(\frac{1}{2}\right)}^3{\left(\frac{1}{2}\right)}^2{+}_4^{5}C{\left(\frac{1}{2}\right)}^4{\left(\frac{1}{2}\right)}^1{+}_5^{5}C{\left(\frac{1}{2}\right)}^5{\left(\frac{1}{2}\right)}^0={\left(\frac{1}{2}\right)}^5{[}_2^{5}C{+}_3^{5}C{+}_4^{5}C{+}_5^{5}C]=\frac{13}{16}$