Aim: How do we use binomial probability?

Complete worksheet

What is a success? What is a failure?

• Successful Trials: (p) getting the wanted outcome

• Failure Trials: (1-p=q) getting the unwanted outcome

Combinations

• Combinations: a selection in which order is not important

!n r

n r

PC

r

Binomial Probability

• In general for a given experiment, if the probability of success in p and the probability of failure is 1 - p = q, then the probability of exactly r successes in n independent trials is

r n rn rC p q

Binominal Probability: “Exactly”

• If a fair coin is tossed 10 times, what is the probability that it falls tails exactly 6 times?– Procedure: • (1) Find the probability of getting the wanted outcome

– P(tails) = 1/2

• (2) Find the probability of getting the unwanted outcome– P(not tails) = 1/2

• Put it into the formula6 4

10 6

1 1 105

2 2 512C

Binomial Probability: “At Least”• A coin is loaded so that the probability of heads is 4 times the probability

of tails. What is the probability of at least 1 tail in 5 throws?– Procedure:

• (1) probability of success– P(tails) = 1/5

• (2) probability of failure– P(not tails) = 4/5

• (3) at least = that number up to the max– P(at least 1 tail in 5) = P(1) + P(2) + P(3) + P(4) + P(5)

• (4) plug in formula and calculate1 4 2 3 3 2 4 1 5 0

5 1 5 2 5 3 5 4 5 5

1 4 1 4 1 4 1 4 1 4

5 5 5 5 5 5 5 5 5 5

2101

3125

C C C C C

Binomial Probability: “at most”• A family of 5 children is chosen at random. What is the probability that

there are at most 2 boys in this family of 5?– Procedure:

• (1) probability of success– P(boys) = 1/2

• (2) probability of failure– P(not boy) = 1/2

• (3) at most = that number down to 0/min– P(at most 2 boys in 5) = P(2) + P(1) = P(0)

• (4) plug in formula and calculate2 3 1 4 0 5

5 2 5 1 5 0

1 1 1 1 1 1

2 2 2 2 2 2

1

2

C C C