7.3 Binomial Trials

• These type of experiments are called:• Binomial Trials• Bernoulli Trials

• The outcomes of a binomial trial are considered as:• Success• Failure

• Since there are only two outcomes, we know that:• Pr(success) + Pr(failure) = 1

• If we call:• Pr(success) = p• Pr(failure) = q

• Then:• p + q = 1 and we can then

say: q = 1 – p

7.3 Binomial Trials• When looking for probabilities,

we use a variable to talk about what we want.

• Example:• If we are tossing a coin 10 times

and consider heads a “success,” then if we are looking for 3 heads, we are looking for Pr(X = 3)

• 5 heads = Pr( )• 3 heads = Pr( )• No more than 4 heads =

Pr( )• 6 tails = Pr( )

• Because Binomial Trials have two options (p or q), there is a specific formula to calculate each situation.

• Here, is the same as C(n, k) that we learned how to calculate before.

• The exponents will add up to be n.• This is just like binomial expansion

that we did earlier, hence the similar name!

Pr k n knX k p q

k

n

k

7.3 Binomial Trials

Find p and q based upon the following situations.• A coin is flipped; heads

• A dice is rolled; even

• A dice is rolled; one

• A dice is rolled; prime

• The recovery rate for a certain disease is 25%

• 61% of married women are in the US labor force

• 52% of students at a university are male

• 76% of cars using toll booths have an easy pass

7.3 Binomial Trials

A fair coin is tossed 5 times. Find the probability of achieving exactly 3 heads.

The recovery rate of a certain cattle disease is 25%. If 30 cattle are afflicted with the disease, what is the probability that exactly 10 will recover?

7.3 Binomial Trials

Each time at bat the probability that a baseball player gets a hit is .300. He comes up to bat four times a game. Find the probability that he gets• Exactly two hits

• At least two hits

7.2 Frequency and Probability Distributions

• Problems to complete from 7.3– Pg. 354 #1 – 6

7.3 Binomial TrialsCalculating Theoretical Probabilities in Binomial Trials

There is going to be a four problem quiz with four options per questions.• What is the n? • What is the p?• What is the q?• What are the possibilities

for k?

Calculate the probabilities.Pr(X = 0) =

Pr(X = 1) =

Pr(X = 2) =

Pr(X = 3) =

Pr(X = 4) =

7.3 Binomial TrialsCreate a Histogram and Pie Chart for the theoretical information.

X Relative Frequency

Degree

0 0.316

1 0.422

2 0.211

3 0.047

4 0.004

Choose the correct answer.1) A B C D

2) A B C D

3) A B C D

4) A B C D

113.76o

151.92o

75.96o

16.92o

1.44o

7.3 Binomial TrialsCreate a Histogram and Pie Chart for the experimental information.

X Relative Frequency

Degree

0

1

2

3

4

Analyze the results!!1) Are there any

discrepencies?2) What does this say about

the test-taker?3) What does this say about

the questions?4) Does…