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warmup
Skills we need
Skills we've learned
86 Binomial Distributions
Find the following probabilities when rolling 3 dice:1) P(exactly 1 three) 2) P(exactly 2 threes)3) P(at least 1 three)
4) Expand
Warmup ans.
Warmup AnswersFind the following probabilities when rolling 3 dice:1) P(exactly 1 three) 2) P(exactly 2 threes)3) P(at least 1 three)
4) Expand
P(1) =
P(2) =
P(1) + P(2) + P(3) =
++ =
Or... 1 P(0) =–
Alg2 Notes 8.6 upload.notebook
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Learning Target
86 Binomial Distributions
1. Use the Binomial Theorem to expand a binomial raised to a power.
2. Find binomial probabilities and test hypotheses.
Determining your chances of winning a marketing contest.
Binomial Theorem
I. Binomial Theorem
1. Expand *see warmup
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You Try
2. Expand
Binomial Experiment
II. Binomial Experiment
A binomial experiment consists of n independent trials whose outcomes are either successes or failures; the probability of success p is the same for each trial, and the probability of failure q is the same for each trial. Because there are only two outcomes, p + q = 1, or q = 1 p.
3) P(exactly 2 heads out of 10 flips) =
P(r) = nCr prqnr p = 0.5 and q = 0.5P(2) = 10C2 (0.5)2(0.5)102
=
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You try
4) Ellen takes a multiplechoice quiz that has 5 questions, with 4 answer choices for each question. What is the probability that she will get at least 2 answers correct by guessing?
P(r) = nCr prqnr
P(at least 2) = P(2) + P(3) + P(4) + P(5)
Or P(at least 2) = 1 [P(0) + P(1)]–
5C0 (0.25)0(0.75)50 5C1 (0.25)1(0.75)511 [ + ]–1 [.23730468 + .3955078] ≈ .367–
You try
5) You make 4 trips to a drawbridge. There is a 1 in 5 chance that the drawbridge will be raised when you arrive. What is the probability that the bridge will be down for at least 3 of your trips?
The probability that the bridge will be down for at least 3 of your trips is 0.8192.
P(3) + P(4) =
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You try
6) A machine has a 98% probability of producing a part within acceptable tolerance levels. The machine makes 25 parts an hour. What is the probability that there are 23 or fewer acceptable parts?
1 [P(25) + P(24)] =–
So
Let's think
Can the binomial theorem find the probability of drawing exactly 2 hearts in a hand of 5 cards?
Pepys wrote a letter to Isaac Newton in 1693 asking about a wager he planned to make. Pepys asked which was more likely: 1. at least one 6 when 6 dice are rolled2. at least two 6's when 12 dice are rolled3. at least three 6's when 18 dice are rolled
see #47 of your homework for this answer
Alg2 Notes 8.6 upload.notebook
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Homework
8.6 p.590 #2, 6, 8, 10, 14, 21, 25, 26 29, 32, 36, 41 43
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