ISRO 2015- probability [Mech]

Question

The probability that a teacher will give an unannounced test during any class is 1/5. If a student is absent twice, then probability that misses at least one test is

(a) 24/25

(b) 16/25

(c) 7/25

(d) 9/25

Answer 1

• The student is absent on two consecutive days.
• The probability NO two consecutive surprised test = $\begin{align*} &\frac{4}{5}*\frac{4}{5} = \frac{16}{25} \\ \end{align*}$
• The probability that the student does not miss these two test = $\begin{align*} \frac{16}{25} \\ \end{align*}$
• The probability that the student misses at least $1$ test = $\begin{align*} 1- \frac{16}{25}  = \frac{9}{25} \\ \end{align*}$