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

Options

• \[ \frac{1}{2} \]

• \[ \frac{1}{4} \]

• \[\frac{1}{8}\]

• \[ \frac{3}{4}\]

Answer 1

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