9. Three cards are drawn at random from a standard deck of 52 card, without replacement. What is the probability of drawing a 7, drawing a 9, and a king in that order?

If the events are independent, the probability of both/all events occurring is determined by multiplying the probabilities of the individual events. For subsequent picks, the deck lacks one more card.

4/52 * 4/51 * 4/50 = ?

8/16575

8/16575 = .000483

To find the probability of drawing a 7, a 9, and a king in that order, we can break it down into three steps and multiply the probabilities for each step.

Step 1: Probability of drawing a 7
A standard deck of 52 cards contains 4 sevens. So, the probability of drawing a 7 as the first card is 4/52.

Step 2: Probability of drawing a 9, given that a 7 was already drawn
After removing the first card, there are now 51 cards remaining in the deck. Among them, there are 4 nines. Therefore, the probability of drawing a 9 as the second card is 4/51.

Step 3: Probability of drawing a king, given that a 7 and a 9 were already drawn
With 50 cards left in the deck, there are 4 kings. So, the probability of drawing a king as the third card is 4/50.

Now, to find the probability of all three events occurring in order, we multiply the individual probabilities together:
(4/52) * (4/51) * (4/50) = 64/132,600, which can be simplified to 1/2,075.

Therefore, the probability of drawing a 7, drawing a 9, and a king in that order is 1/2,075.