Question

A coin is tossed and a card is selected at random from a well shuffled pack of 52 playing cards. The probability of getting head on the coin and a face card from the pack is:

• A. $\frac{2}{3}$
• B. $\frac{3}{26}$
• C. $\frac{9}{52}$
• D. $\frac{1}{26}$

Hint:

When multiple independent events occur, multiply their individual probabilities to find the total probability.

Answer 1

The Correct Option is D

The probability of flipping heads on a coin is $\frac{1}{2}$. The probability of drawing a face card from a 52-card deck, which contains 12 face cards, is $\frac{12}{52}$, simplifying to $\frac{3}{13}$. Consequently, the combined probability of these two independent events occurring is: \[ P(\text{Head and face card}) = \frac{1}{2} \times \frac{3}{13} = \frac{3}{26} \] The final probability is therefore $\frac{3}{26}$.