Question

Three cards are drawn from a deck of 52 cards with replacement, what is the

probability of getting:

i. At most one face card​

Answer 1

Answer:

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Step-by-step explanation:

Let’s let event A = “at least one face card” and let event B = “no face cards.” Probability of A can be difficult to find directly, but since p(A) + p(B) = 1 (in other words, the only possibilities can be zero, or at least one), we can find p(B) much more easily.

So p(B) is “no face cards”, so first must not be face and second and third.

Since the cards are replaced each time, they are independent probabilities. Each one being non-face is 40/52 because the entire deck is selected from, not just one suit). Since the probabilities are independent, you simply multiply.

So the p(B) = p(none are face cards) = (40/52)^3 = .455

Last step (this is easy to forget to do so be careful) p(B) = .455 and p(A)+p(B)=1, therefore you subtract .455 from 1 to get your final answer .545