##### Question

In: Statistics and Probability

# A six sided die is rolled 4 times. The number of 2's rolled is counted as...

A six sided die is rolled 4 times. The number of 2's rolled is counted as a success.

1. Construct a probability distribution for the random variable.

 # of 2's P(X)
1. Would this be considered a binomial random variable?
2.    What is the probability that you will roll a die 4 times and get a 2 only once?

d Is it unusual to get no 2s when rolling a die 4 times? Why or why not? Use probabilities to explain.

## Solutions

##### Expert Solution

a) P(2) = 1/6

# of 2's                 Probability

0                         (1 - 1/6)4 = 0.4823

1                        4C1 * (1/6) * (5/6)3 = 0.3858

2                        4C2 * (1/6)2 * (5/6)2 = 0.1157

3                        4C3 * (1/6)3 * (5/6)1 = 0.0154

4                        (1/6)4 = 0.0008

b) Yes this is a binomial distribution

c) P(X = 1) = 0.3858

d) P(X = 0) = 0.4823

Since probability is not less than 0.05 or greater than 0.95, this is not an unusual event. So it is not unusual to get no 2s when rolling a die 4 times

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