Binomial distribution

Which three criteria do binomial experiments meet?
There are only two trials.

The trials are independent.

There are only two outcomes per trial.

Each outcome is repeatable.

The probability of success is the same for each trial.

The trials are independent.

There are only two outcomes per trial.

The probability of success is the same for each trial.

Use the features on the left to identify which of the following are binomial experiments.

a survey asking 50 people their favorite food

a survey asking 50 people if they like pizza

a survey measuring 50 people to see if they are over 6 feet tall

a test of rolling a number cube 50 times and recording the result

a survey asking 50 people if they like pizza

a survey measuring 50 people to see if they are over 6 feet tall

You already learned the expression for calculating binomial probabilities:

Image of Binomial Formula
What does each variable represent?

n represents the .

p represents the .

k represents

n represents the . Number of trials

p represents the . Probability of success

k represents number of successes

Determine the values of the variables in the binomial probability formula for the following statement: What is the probability of getting exactly 5 "heads" in 10 coin flips?
n =
p =
k =

N=10
P=0.5
K=5

Use the following formula for calculating binomial probabilities to answer the question.

Image of Binomial Formula

What is the probability of getting exactly 5 "heads" in 10 coin flips?

1/32

63/256

1/2

193/256

B)63/256

Which expression represents the probability of rolling a 5 exactly three times in ten rolls of a number cube with six sides?

Answer C

A number cube with six sides is rolled seven times. The probability of getting a 4 exactly twice is

0.234

Peter guesses on all 10 questions of a multiple-choice quiz. Each question has 4 answer choices, and Peter needs to get at least 7 questions correct to pass. Here are some probabilities computed using the binomial formula:

P(getting exactly 7 correct) = 0.0031

P(getting exactly 8 correct) = 0.000386

P(getting exactly 9 correct) = 2.86 × 10−5

P(getting exactly 10 correct) = 9.54 × 10−7

Using the information on the left, combine the individual probabilities to compute the probability that Peter will pass the quiz.

0.001

0.002

0.0035

0.005

0.0035

P(getting exactly 7 correct) = 0.0031

P(getting exactly 8 correct) = 0.000386

P(getting exactly 9 correct) = 2.86 × 10-5

P(getting exactly 10 correct) = 9.54 × 10-7

Describe the pattern in the probability of getting greater numbers of successes.

The probability gets smaller and approaches 0 because 9 or 10 successes in 10 trials is unlikely.

According to a survey, 40% of adults watch a particular television show. Six adults are selected at random. The binomial distribution below shows the probability that k out of 6 adults watch the television show.

P(k = 0) = 0.0467

P(k = 1) = 0.1866

P(k = 2) = 0.3110

P(k = 3) = 0.2765

P(k = 4) = 0.1382

P(k = 5) = 0.0369

P(k = 6) = 0.0041

The distribution is

symmetric.

skewed.

both symmetric and skewed.

The sum of the probabilities in the distribution is
.

Skewed

The sum is 1.

Find the probability that you will roll an even number exactly 5 times when you:

roll a six-sided number cube 10 times.
P =
roll a six-sided number cube 20 times.
P =

Explain why the second result is less.

0.246

0.015

As the number of trials changes, the distribution changes. Since there is a 50% chance of rolling an even number, having a small number of successes is less likely when the number of rolls increases.