Correct answer only !

a spinner has five equal sections that are numbered 1 through 5.

in which distributions does the variable x have a binomial distribution?

select each correct answer.

when the spinner is spun three times, x is the sum of the numbers the spinner lands on.

when the spinner is spun multiple times, x is the number of spins until it lands on 5.

when the spinner is spun four times, x is the number of times the spinner does not land on an odd number.

when the spinner is spun five times, x is the number of times the spinner lands on 1.

 C & D

Step-by-step explanation:

A binomial experiment must satisfy ALL four of the following:

 A fixed number of trials  Each trial is independent of the others  There are only two outcomes (Success & Fail)  The probability of each outcome remains constant from trial to trial.

A) When the spinner is spun three times, X is the sum of the numbers the spinner lands on.

  → #3 is not satisfied  (#4 is also not satisfied)

B) When the spinner is spun multiple times ...

    → #1 is not satisfied

C)  When the spinner is spun four times, X is the number of times the spinner does not land on an odd number.

    → Satisfies ALL FOUR

 A fixed number of trials = 4  Each trial is independent of the others = each spin is separate  There are only two outcomes = Not Odd & Odd  The probability of each outcome remains constant from trial to trial = P(X = not odd) = 0.50 for each spin

D) When the spinner is spun five times, X is the number of times the spinner lands on 1.

   → Satisfies ALL FOUR

 A fixed number of trials = 5  Each trial is independent of the others = each spin is separate  There are only two outcomes = 1 & Not 1  The probability of each outcome remains constant from trial to trial = P(X = 1) = 0.17 for each spin