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 the deck. 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 seven, the second card drawn is a seven, and the third card drawn is a face card? do not round your intermediate computations. round your final answer to four decimal places.

Question

contestada

Respuesta :

ayune ayune · Answer 1 · 2022-11-25T14:50:29+01:00

Three cards are randomly drawn from a standard deck. The probability it will be 7, 7, and face cards subsequently is 0.0011

The formula for the conditional probability is given by:

P(A∩B) = P(A|B) . P(B)

Where:

P(A∩B) = probability of A and B occur

P(A|B) = Probability of A occurs if B occurs

P(B) = probability of B occurs

In the given problem, the standard deck has 52 cards. Three cards are drawn subsequently from the deck.

1st draw:

There are 4 cards in the deck with number 7, hence:

P(7) = 4/52 = 1/13

2nd draw:

The remaining cards now = 51.

Suppose the first card is 7, then the probability the 2nd card is also 7 is:

P(7 | 7) = 3/51 = 1/17

3rd draw:

Suppose the first and the second cards are 7.

Number of face cards = 3 x 4 = 12

remaining cards = 50.

Hence,

P(face |(7|7)) = 12/50 = 6/25

Finally,

P(7,7,face) = 1/13 x 1/17 x 6/25 = 6/5525 = 0.0011

Learn more about conditional probability here:

https://brainly.com/question/28545104

#SPJ4