In an examination, the probability of a candidate solving a question is 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?

Concept:

• \(P(X=r)=n_{c_{r}}(p)^{r}(q)^{n-r}\)
• Required probability = 1 - Not required probability

Calculation:

Here number of attempt (n) = 5

p = 1/2 and q = 1/2

P(X is greater than equal to 2) = 1 - P (X < 2) = 1 - P(X = 0) - P(X = 1)

∴ Required probability = 1 - P(X = 0) - P(X = 1)

 \(\begin{array}{l} \quad 1-{ }^{5} C_{0}\left(\frac{1}{2}\right)^{0}\left(\frac{1}{2}\right)^{5}-{ }^{5} C_{1}\left(\frac{1}{2}\right)^{1}\left(\frac{1}{2}\right)^{4} \\ \Rightarrow 1-\left(\frac{1}{2}\right)^{5}-5\left(\frac{1}{2}\right)^{5} \\ \Rightarrow 1-\left(\frac{1}{2}\right)^{5}[1+5] \\ \Rightarrow 1-\frac{6}{32} \\ \Rightarrow \frac{13}{16} \end{array}\)

Hence, option (4) is correct.