Practice quiz answers using a tree diagram

Suppose that you have a bag with 4 green chips and 3 yellow chips.

1. If you choose two chips with replacement (you put the first chip back in the bag before drawing the second chip),
A. What is the probability that you will get two greens?
B. What is the probability that you will get two yellows?
C . What is the probability that you will get one of each color?

With replacement probabilities:

Prob of getting green on first pick:
4 greens out of 7 chips
4/7 (vertical lines)

 Prob of getting another green if the first one is green:
4 greens out of 7 chips
4/7 (horizontal lines)		 Prob of getting a yellow if the first one is green
3 yellow out of 7 chips
3/7 (horizontal lines)
Prob of getting yellow on first pick
3 yellow out of 7 chips
3/7 (vertical lines)		 Prob of getting green if the first one is yellow:
4 greens out of 7 chips
4/7 (horizontal lines)		 Prob of getting another yellow if the first one is yellow:
3 yellow out of 7 chips
3/7 (horizontal lines)

(these fractions can't be simplified)

2. If you choose two chips without replacement (you keep the first chip out of the bag while drawing the second chip),
A. What is the probability that you will get two greens?
B. What is the probability that you will get two yellows?
C . What is the probability that you will get one of each color?

Prob of getting green on first pick:
4 greens out of 7 chips
4/7 (vertical lines)

 Prob of getting another green if the first one is green:
3 greens out of 6 chips
3/6 (horizontal lines)		 Prob of getting a yellow if the first one is green
3 yellow out of 6 chips
3/6 (horizontal lines)
Prob of getting yellow on first pick
3 yellow out of 7 chips
3/7 (vertical lines)		 Prob of getting green if the first one is yellow:
4 greens out of 6 chips
4/6 (horizontal lines)		 Prob of getting another yellow if the first one is yellow:
2 yellow out of 6 chips
2/6 (horizontal lines)

Do more practice with square area diagrams With replacement / without replacement