Question

Mark the correct alternative in the following question:
Two cards are drawn from a well shuffled deck of 52 playing cards with replacement. The probability that both cards are queen is

Options

• \[ \frac{1}{13} \times \frac{1}{13}\]

• \[\frac{1}{13} + \frac{1}{13}\]

• \[\frac{1}{13} \times \frac{1}{17}\]

• \[\frac{1}{13} \times \frac{4}{5}\]

Answer 1

\[\text{ Let } : \]

\[\text{ A be the event that a queen is drawn in the first draw and } \]

\[\text{ B be the event that a queen is drawn in the second draw as well} \]

\[\text{ Now } , \]

\[P\left( \text{ Both the two cards drawn are queen } \right) = P\left( A \right) \times P\left( B|A \right)\]

\[ = \frac{4}{52} \times \frac{4}{52}\]

\[ = \frac{1}{13} \times \frac{1}{13}\]