SOLUTION: It is found that when a particular 4-sided die is rolled a 1 occurs 24.2% of the time, a 2 occurs 26.3% of the time, a 3 occurs 27.1% of the time, and a 4 occurs 22.4% of the time.

Question 947929: It is found that when a particular 4-sided die is rolled a 1 occurs 24.2% of the time, a 2 occurs 26.3% of the time, a 3 occurs 27.1% of the time, and a 4 occurs 22.4% of the time.
a.) If the die is rolled 32 times, what is the probability that an even number occurs exactly 16 times?
b.)What is the expected value of a single roll of the die?
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
It is found that when a particular 4-sided die is rolled a 1 occurs 24.2% of the time, a 2 occurs 26.3% of the time, a 3 occurs 27.1% of the time, and a 4 occurs 22.4% of the time.
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P(even) = 26.3%+22.4% = 48.7%
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a.) If the die is rolled 32 times, what is the probability that an even number occurs exactly 16 times?
Ans: P(x = 16) = 32C16*(0.487^16)*(0.513^16) = binompdf(32,0.487,16) = 0.1384
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b.)What is the expected value of a single roll of the die?
E(x) = 0.242*1 + 0.263*2 + 3*0.271*3 + 4*0.224 = 2.477
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Cheers,
Stan H.
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