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 in problem , 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)

Here,

p(odd) = P(1) + P(3) = 0.243 + 0.233 = 0.476

Note that the probability of x successes out of n trials is          
          
P(n, x) = nCx p^x (1 - p)^(n - x)          
          
where          
          
n = number of trials =    30      
p = the probability of a success =    0.476      
x = the number of successes =    13      
          
Thus, the probability is          
          
P (    13   ) =    0.130567025 [ANSWER]

*********************

b)

Consider:

Thus,  
  
E(x) = Expected value = mean = Sum(xP(x)) = 2.502 [ANSWER]

Related Questions

Navigate

• Browse (All)
• Browse I
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.