Question

If two cards are drawn from a deck, what is the probability that exactly one of the cards will be a face card?

Answer 1

The probability of getting exactly one face card is 0.72.

According to the questions two cards are drawn from a deck.

Since, we know that

Total number of cards in a deck = 52

Total number of face cards =  3 × 4 = 12

So, the number of ways of selecting 2 cards from a deck = $^{52} C_{2}$

And, the total number of ways of  getting exactly one face cards

= $^{12} C_{1} \times ^{40} C_{1}$  + $^{40} C_{1} \times ^{12} C_{1}$

= 2$^{40} C_{1} \times ^{12} C_{1}$

Therefore, the probability of getting exactly one face card

= $\frac{2(^{40} C_{1} \times ^{12} C_{1})}{^{52C_{2} } }$

$= \frac{2(\frac{40 \times 39!}{1!\times 39!} \frac{12\times 11!}{11!}) }{\frac{52\times 51\times 50!}{2!\times50!} }$

$= \frac{2(40\times 12)}{26\times 51}$

$=\frac{2\times 480}{1326}$

= 0.72

Hence, the probability of getting exactly one face card is 0.72.

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https://brainly.com/question/13293035

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