Question 1 a) Consider rolling a fair six-sided die 5 times. True or false: The

Question

Question 1

a) Consider rolling a fair six-sided die 5 times. True or false: The number of times that the die lands with an even number of spots have a binomial distribution with the number of trials n being 5, and the probability of a success being 1/2.

b) Consider rolling a fair six-sided die 5 times, and then tossing a fair coin 5 times. Assume that all the tosses and rolls are independent. True or false: The number of tails in all the tosses plus the number of times that the die lands with an even number of spots ________________________. (choose from below)

Explanation / Answer

a)

When we roll a fair die possible outcomes are 1, 2, 3, 4, 5, 6.

Out of these 6 possible outcomes, 3 are even and 3 are odd.

So

P(even) = 3/6 = 1/2

That is the number of times that the die lands with an even number of spots have a binomial distribution with the number of trials n being 5, and the probability of a success being 1/2.

Hence, asnwer: true

b)

Sum of two binomial variable with same p and number of trials n1 and n2 will be a binomial variable with parameters p and n1+n2.

So correct option is "has a binomial distribution with n = 10 and p = 1/2"

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