Q; Which of the following is an example of a binomial distribution?

Question

Which of the following is an example of a

binomial distribution? Please explain.

A. probabilities of the number of queens in

a five-card hand

B. probability of each sum when two dice

are rolled

C. probability of each lane for a 100 m race

D. probabilities of the number of times a 5

occurs when spinning a spinner six times

Answer 1

D. is the best example of a binomial distribution.

Binomial distributions have a few important properties:

1. They apply to a situation where an outcome or observation is repeated, and the relevant probability is the success or failure of an outcome in particular. None of A, B, or C have a clear yes/no outcome.
2. The number of trials are fixed. Neither B nor C give the number of trials, so both of those are out.
3. Each observation is independent.
4. The probability of success is the same between trials.

So that leaves D! It has a yes/no outcome (whether the spinner lands on 5), it has repeated observations (successive spins), the number of trials is fixed (six spins), successive spins are independent, and the probabilities are the same on each spin.

Hope that helps!