SOLUTION: A 4-sided die is rolled. A 1 occurs 27.9% of the time, a 2 occurs 23.5% of the time, a 3 occurs 26.6% of the time, and a 4 occurs 22.0% of the time. a) If the die is rolled 26 tim

Question 982731: A 4-sided die is rolled. A 1 occurs 27.9% of the time, a 2 occurs 23.5% of the time, a 3 occurs 26.6% of the time, and a 4 occurs 22.0% of the time.
a) If the die is rolled 26 times, what is the probability that an even number occurs exactly 12 times?
b) What is the expected value of a single roll of the die?

Answer by mathmate(429) (Show Source): You can put this solution on YOUR website!

Given:
A 4-sided die, with the following pmf:
1: 0.279
2: 0.235
3: 0.266
4: 0.220
(Total=1.000)

(a) Rolled 26 times, need probability that an even number occurs exactly 12 times.
(b) Find expected value of a single roll of the die.

Solution:
(A) Probability of getting an even number 12 times out of 26 tosses.
Probability of getting an even number at each toss,
p = P(2)+P(4)=0.235+0.220=0.455

To find probability of rolling an even number 12 times out of 26, we use binomial theorem:

Therefore

(B) Expected value of a single throw E[X]
Using the standard formula,
E[X]=sum x*p(x)=
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