Elementary Statistics – Probability Examples

Example 1

An unfair die is rolled once and the upward face is recorded. The faces have the following probabilities:

Face	1	2	3	4	5	6
Probability	0.125	0.25	0.125	0.25	0.125	0.125

1. What is the probability of rolling an even number?

2. What is the probability of rolling something other than a two?

3. If this were a fair die, what would be the probability of rolling each face?

Example 2

An unfair coin is flipped twice and the faces are recorded. For this coin, P(“heads”) = ¼ and P(“tails”) = ¾ .

1. What is the probability of getting exactly one head?

2. Suppose the coin is flipped three times. What is the probability that there will be a mixture (any mixture) of heads and tails?

Example 3

Suppose a fair 4-sided die is rolled twice, and each time the down-face is recorded

.

1. What is the probability that the first roll is a 2 or the sum of the rolls is 2?

2. What is the probability that the first roll is a 2 or the sum of the rolls is 4?

3. Suppose we know the sum of the rolls is 4. Then what is the conditional probability that the first roll is a 1?

4. Given that the same number occurs on both rolls, what is the conditional probability that the first roll is a 2?

5. Are the events {sum of the rolls is 4} and {first roll is 1} independent? What about the events {same number on both rolls} and {first roll is 2}?

Example 4

There are 6 jelly beans in a bag: 4 blue and 2 yellow. Two jelly beans are drawn at random (and without replacement) from the bag.

1. What is the probability that both jelly beans are yellow?

2. What is the probability that exactly one of the jelly beans is yellow?