Question

There are $2$ groups of subjects one of which consists of $5$ science subjects & $3$ engg. subjects & other consists of $3$ science & $5$ engg. subjects. An unbiased die is cast. If the number $3$ or $5$ turns up a subject is selected at random from first group, otherwise the subject is selected from $2^{nd}$ group. Find the probability that an engg. subject is selected.

• A. $\frac{13}{24}$
• B. $\frac{1}{8}$
• C. $\frac{5}{12}$
• D. $\frac{11}{24}$

Answer 1

The correct option is A $\frac{13}{24}$

Two groups
Ist Group $5$ Science & $3$ Engg.
IInd Group $3$ Science & $5$ Engg.
When a die is tossed
$P\left(A\right)$: probability that $3$ or $5$ appears.
$P\left(A\right)=\frac{2}{6},P\left(\overline{A}\right)=\frac{4}{6}$
Probability that an engg. subject selected when die is tossed $=\frac{2}{6}\times \frac{3}{8}+\frac{4}{6}\times \frac{5}{8}=\frac{26}{48}=\frac{13}{24}$