A card is chosen at random from a deck of 52 cards. It is replaced, and a second card is chosen. What is the probability that both cards chosen are jacks?

Question

anonymous · Answer

Well, there are 4 jacks in every deck of cards. So the probability would be 4/52 which is 1/13.

anonymous · Answer

It's true that the probability of drawing a jack is 1/13, and we need this information, but we aren't done.

If 1/13 is the probability of drawing a jack on a single draw, how would we find the probability of drawing a jack twice in two draws?

anonymous · Answer

Thank you so much for helping me> this quiestion was really difficult since I have no idea how deck cards work. Thanky you :D

anonymous · Answer

It is still 1/13 because they put the card back, "it is replaced"

anonymous · Answer

It is not 1/13. That only looks at a single draw. We are looking at two draws with replacement.

whpalmer4 · Answer

There are two events here.  The first event has p=1/13 of drawing a jack.  The second one also has p=1/13 of drawing a jack, but we want to know the p of drawing a jack followed by drawing another jack.  To do this, we multiply the probabilities of the independent events.

anonymous · Answer

Since we are replacing the card, the first draw doesn't effect the second draw, so the probability to draw a jack the first time is 1/13, and it's also 1/13 to draw the second jack.

Since these are independent events, we know:

$$P(A&B) = P(A)P(B)$$

So, if A is drawing a jack on the first draw, and B is drawing a jack on the second draw, then:

$$P(2Jacks) = P(Jack,Draw1)P(Jack,Draw2)$$

P(Jack,Draw1) = P(Jack,Draw2) = 1/13

So we can just plug those in.

anonymous · Answer

Does that make sense?

anonymous · Answer

Yes  that makes much better sence   Thank you