Binomial Distributions Quiz

In this quiz, you will simulate coin flips using np.random.binomial to compute proportions for the following outcomes.

1. A fair coin flip produces heads
2. Five fair coin flips produce exactly one head
3. Ten fair coin flips produce exactly four heads
4. Five biased coin flips with P(H) = 0.8 produce exactly five heads
5. Ten biased coin flips with P(H) = 0.15 produce at least three heads

Then, you'll compare these proportions with probabilities in the quizzes below.

QUIZ QUESTION: :

Use the proportions you observed in your simulation data above to state the probability of each of the following outcomes.

ANSWER CHOICES:

A fair coin flip produces heads

Five fair coin flips produce exactly one head

Ten fair coin flips produce exactly four heads

Five biased coin flips with P(H) = 0.8 produce exactly five heads

Ten biased coin flips with P(H) = 0.15 produce at least three heads

Outcome	Probability
0.180
0.5
0.205
1
0.45
0.130
0.2
0.156
0.328
0

SOLUTION:

Outcome	Probability
0.180	Ten biased coin flips with P(H) = 0.15 produce at least three heads
0.5	A fair coin flip produces heads
0.205	Ten fair coin flips produce exactly four heads
0.156	Five fair coin flips produce exactly one head
0.328	Five biased coin flips with P(H) = 0.8 produce exactly five heads

Compute the probabilities of each of the five outcomes above mathematically. Do these match with the proportions you found in your simulated data?

Yes

No

SOLUTION:

Yes