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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 :

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

[tex]P(F)=\frac{12}{52}=0.2308[/tex]

The probability of picking the second card without replacement is

[tex]P(E)=\frac{5}{51}=0.09804[/tex]

The Probability of picking the third card is five is

Total number of 5 = 4

[tex]P(B)=\frac{4}{50}=0.08[/tex]

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

[tex]\begin{gathered} P(F)\times P(E)\times P(B) \\ \frac{12}{52}\times\frac{5}{51}\times\frac{4}{50}=0.001809 \end{gathered}[/tex]

The probability is 0.0018

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