Question

1. Assume we have a small jar full of 140 perfectly shaped jelly beans. Fifty of the jelly beans are red, 45 of the jelly beans are green, and 35 of the jelly beans are purple and 20 are black. If you randomly select one jelly bean, then …

1. What is the probability the jelly bean is red?
2. What is the probability the jelly bean is black?
3. What is the probability the jelly bean is green?
4. What is the probability the jelly bean is purple?
5. What is the probability you do not select a red jelly bean?
6. What is the probability the jelly bean is red or green?
7. What is the probability you do not select a red or green jelly bean?
8. Assume you pick a red jelly bean. Rather than put the jelly bean back in the jar, you eat it! You then randomly select another jelly bean from the jar.

1. What’s the probability that the jelly bean you select this time is red?
2. What’s the probability that the jelly bean you select this time is green?

3. What’s the probability that this jelly bean is not green?

Answer 1

Fifty of the jelly beans are red, 45 of the jelly beans are green, and 35 of the jelly beans are purple and 20 are black.

a. What is the probability the jelly bean is red?

P[ red jelly bean ] = number of red jelly beans / total number of jelly beans

P[ red jelly bean ] = 50/140

P[ red jelly bean ] = 5/14

b. What is the probability the jelly bean is black?

P[ black jelly bean ] = number of black jelly beans / total number of jelly beans

P[ black jelly bean ] = 20/140

P[ black jelly bean ] = 1/7

c.What is the probability the jelly bean is green?

P[ green jelly bean ] = number of green jelly beans / total number of jelly beans

P[ green jelly bean ] = 45/140

P[ green jelly bean ] = 9/28

d. What is the probability the jelly bean is purple?

P[ purple jelly bean ] = number of purple jelly beans / total number of jelly beans

P[ purple jelly bean ] = 35/140

P[ purple​​​​​​​​​​​​​​ jelly bean ] = 1/4

e. What is the probability you do not select a red jelly bean?

P[ not red jelly bean ] = 1 - P[ red jelly bean ]

P[ not red jelly bean ] = 1 - 5/14

P[ not red jelly bean ] = 9/14

f. What is the probability the jelly bean is red or green?

P[ jelly bean is red or green ] = P[ red jelly bean ] + P[ green jelly bean ]

P[ jelly bean is red or green ] = 5/14 + 9/28

P[ jelly bean is red or green ] = 19/28

g. What is the probability you do not select a red or green jelly bean?

P[ not select a red or green jelly bean ] = 1 - P[ jelly bean is red or green ]

P[ not select a red or green jelly bean ] = 1 - 19/28

P[ not select a red or green jelly bean ] = 9/28

h. Assume you pick a red jelly bean. Rather than put the jelly bean back in the jar, you eat it! You then randomly select another jelly bean from the jar.

49 of the jelly beans are red, 45 of the jelly beans are green, and 35 of the jelly beans are purple and 20 are black.

Total = 139

i) What’s the probability that the jelly bean you select this time is red?

P[ red jelly bean ] = number of red jelly beans / total number of jelly beans

P[ red jelly bean ] = 49/139

ii) What’s the probability that the jelly bean you select this time is green?

P[ green jelly bean ] = number of green jelly beans / total number of jelly beans

P[ green jelly bean ] = 45/139

iii) What’s the probability that this jelly bean is not green?

P[ jelly bean is not green ] = 1 - P[ green jelly bean ]

P[ jelly bean is not green ] = 1 - 45/139

P[ jelly bean is not green ] = 94/139