Question

You have a four-card deck containing a king, a queen, a jack, and a three. You draw a random card, then put it back and draw a second random card. Use a tree diagram to calculate the probability that you draw exactly one "face" card (a king or a queen or a jack).

I have a bunch of problems like this one, and I don't understand how to do them-_-

Answer 1

For your first draw you have 4 possibilities:
K
Q
J
3
On your second draw, you again have the same four possibilities, since you put the card back, therefore you have 16 different cases:
First Choice--> Second Choice
K-->K, Q, J, or 3
Q-->K, Q, J, or 3
J-->K, Q, J, or 3
3-->K, Q, J, or 3
You want to find the probability of choosing exactly one face card, that means if you choose a face card first, you have to choose the 3 on your second draw. However, if you draw a 3 first, your second draw can be a K, Q, or J. So add 1+1+1+3=6 out of a total of 16 different cases. So the probability is 6/16.

The key to solving these types of problems is to list all the possibilities that can happen and choosing the cases that match the description.

Hope this helps!

Answer 2

Yeah that totally helps! Thanks you so much!

Answer 3

3/8