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:

0.2

0.45

0.328

0.205

0.180

1

0.130

0

0.156

0.5

Outcome	Probability
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

SOLUTION:

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

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