Question

A card is drawn at random from a standard deck. That card is not put back in the deck, and a second card is drawn at random from the remaining cards in thedeck. Neither of the cards drawn so far are put back in the deck, and a third card is drawn at random from the remaining cards in the deck.What is the probability that the first card drawn is a face card, the second card drawn is a five, and the third card drawn is a five?Do not round your intermediate computations. Round your final answer to four decimal places.

Answer 1

This probability without replacement

Let the probability of first card=P(F)

probability of the second card=P(E)

probability of the third card=P(B)

The total outcome is 52

Total face card =12

The probability of face card is

`P(F)=(12)/(52)=0.2308`

The probability of picking the second card without replacement is

`P(E)=(5)/(51)=0.09804`

The Probability of picking the third card is five is

Total number of 5 = 4

`P(B)=(4)/(50)=0.08`

The probability of the first card, second card, and third card is

`\begin{gathered} P(F)* P(E)* P(B) \\ (12)/(52)*(5)/(51)*(4)/(50)=0.001809 \end{gathered}`

The probability is 0.0018