"if two cards are drawn at random without replacement from a standard deck, find the probability that the second card is a face card, given that the first card was a queen. a. 3/13b. 4/17c. 11/51d. 5/17"

C.

Step-by-step explanation:

it is to be noted that the question is only asking for the probability of the 2nd card given that the first card was queen , and not asking for the probability of 1st card to be queen and 2nd card to be faced card

we can represent it in an expression:

here P(Q) is the first event: Queen

and P(F|Q) is the second event: Faced card, given that the Queen is taken

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we only need to know what is P(F|Q), and that can be found directly found:

let's start with P(Q), what is the probability that the first card is a Queen? Well, there are 4 queens in a standard deck of 52 cards, so the probability should be:

now we have taken our queen, but we haven't put it back in the deck. so the amount of cards in the deck now are 51.

let's calculate P(F|Q),now that one queen is taken out, what is the probability of the next card to be a faced card? Well, in a standard deck there are 12 faced cards, but in our case one queen is already taken out, so there are 11 faced cards in our deck!

and this our answer!

the correct answer is 5 6 and 7