It is found that when a particular 4-sided die is rolled a 1 occurs 24.3% of the

Question

It is found that when a particular 4-sided die is rolled a 1 occurs 24.3% of the time, a 2 occurs 26.8% of the time, a 3 occurs 23.3% of the time, and a 4 occurs 25.6% of the time.

a) If the die is rolled 30 times, what is the probability that an odd number occurs exactly 13 times?

b) What is the expected value of a single roll of the die?

For the die above, let the random variable X be defined as X = (the number of times that a 2 occurs). If the die is rolled a total of three times:

a) Construct a table and histogram for the probability distribution of X.

b) Find E(X).

Explanation / Answer

a) we have 2 odd numbers 1 and 3

total probabilities of coming an odd number = 0.243+0.233 = 0.476

probability of coming non odd numbers = 0.524

n = 30

probability that 13 times number come up

30c13*(0.476)^13*(0.524)^17 = 0.130

b)e(x) = 1*0.243 + 2*0.268 + 3*0.233 + 4*0.256 = 2.502

c)two comes up in three times = 0.268^3 = 0.019

d)expected value of 2 will be 2*0.268 = 0.536

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