Question

Mark the correct alternative in the following question:

A die is thrown and a card is selected at random from a deck of 52 playing cards. The probability of getting an even number of the die and a spade card is

$\left(\mathrm{a}\right)\frac{1}{2}\left(\mathrm{b}\right)\frac{1}{4}\left(\mathrm{c}\right)\frac{1}{8}\left(\mathrm{d}\right)\frac{3}{4}$

Answer 1

$$\begin{gathered} \mathrm{Let}: \\ A\mathrm{be}\mathrm{the}\mathrm{event}\mathrm{of}\mathrm{getting}\mathrm{an}\mathrm{even}\mathrm{number}\mathrm{of}\mathrm{the}\mathrm{die}\mathrm{and} \\ B\mathrm{be}\mathrm{the}\mathrm{event}\mathrm{of}\mathrm{getting}\mathrm{a}\mathrm{spade}\mathrm{card} \\ \mathrm{Now}, \\ \mathrm{P}\left(\mathrm{getting}\mathrm{an}\mathrm{even}\mathrm{number}\mathrm{of}\mathrm{the}\mathrm{die}\mathrm{and}\mathrm{a}\mathrm{spade}\mathrm{card}\right)=\mathrm{P}\left(AB\right) \\ =\mathrm{P}\left(A\right)\times \mathrm{P}\left(B|A\right) \\ =\frac{3}{6}\times \frac{13}{52} \\ =\frac{1}{8} \end{gathered}$$

Hence, the correct alternative is option (c).