1 Suppose a die is rolled 3 time and the outcome is recorded

1) Suppose a die is rolled 3 time and the outcome is recorded for teach roll.

a) How many different results can be recorded from this set of 3 rolls?

b) How many results will have a different number up for each of the three rolls?

c) How many rolls will have at least 2 sets the same?

d)What is the probability of rolling a 1 while rolling 1 die three times in a row?

e) What is the probability of the sum of your dice totaling 5 while rolling 2 dice?

f) In an example where you were rolling a set of 10 dice 3 times. What is the probability of getting a 1 or 2 in each of the 3 rolls? (hint, use the binomial equation to make this easy)

Solution

a) 6^3 = 216 outcomes

b) 6(5)(4) =120 outcomes

c) 3(6^2)5 = 540

d) Prob rolling 1 3 times = 1/6^3

e) Prob (sum =5 for two dice)

= P(1,4)+P(2,3)+P(3,2)+P(4,1)

= 4/36 = 1/9

f) 10 dice 3 times

P(1 or 2 in 3 rolls )

p = prob for one throw success = 2./6 = 1/3

X no of one or 2 is binomial with n = 10 and p = 1/3

P(X= 3) = 0.2601