Section 5.2

Binomial Probabilities

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Features of a Binomial Experiment

1. There are a fixed number of trials, n2. The n trials are independent and repeated3. Each trial has only two outcomes: success, S, and

Failure, F4. The probability of success is the same for each trial

- Prob. of S = p- Prob. of F = 1 – p = q

5. The goal is to find the probability of r successes out of n trials

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Ex: 1

3 multiple-choice questions. Each question has 4 choices, only one is correct. You randomly choose an answer for each.a)P(success for each question) =

P(failure for each question) =

b) List out all the outcomes and their probabilities:

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Probabilities for Binomial Experiments Formula

n: # of trialsp: probability of successq: probability of failurer : # of success (random variable of interest)

Use it to compute P(1 out of 3 questions correct):

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Ex: 2

59% of Internet users are worried about their email privacy. a) Find P(out of 10 users, 6 are worried).

b) Find P(r ≤ 5).

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Using Binomial Distribution in Calculator2nd Vars (distr) (to find exact # of successes) binompdf(n, p, r) (to find # of success or less) binomcdf(n, p, r)Try: for n = 6 and p = 0.50P (r = 4) =

P(r 4) =

P(r ≥ 4) =

P(r < 4) =

P(r > 4) =

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Ex: 3

Seeds of a hybrid tomato have probability 0.70 of germinating. A biologist plants six seeds.

a.) P(exactly four seeds will germinate)

b.) P(at least four seeds will germinate)

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Ex: 4New eye operation known to restore eyesight of 30% of patients.

A new technique for this surgery was successful for 4 of the patients.

Is the new technique better than the old?

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Can you English?•4 or more•At least 4•No fewer than 4•Not less than 4----------------------------•4 or fewer•At most 4•No more than 4•Does not exceed 4----------------------------•More than 4•Exceeds 4-----------------------------•Fewer than 4•Not as large as 4

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