20 A fair die is rolled a fair coin is tossed and a card is

20. A fair die is rolled, a fair coin is tossed, and a card is drawn from a standard deck of 52 playing cards. Assuming these events are independent, what is the probability that the number falling uppermost on the die is a 6, the coin shows a tail, and the card drawn is a face card?

Solution

P( Die rolled a 6 ) = 1/ 6

P(Fair coin tossed tail) = 1/2

P(Card drawn is a face card) = 12 / 52

P( Die rolled a 6 and Fair coin tossed tail and Card drawn is a face card) = 1/6 * 1/2 * 12/52 = 0.01923