Binomial Probabilities: Examples and Calculations, Study notes of Statistics

Examples and calculations using the binomial distribution and binomial table to find probabilities of specific outcomes in multiple bernoulli trials. Topics include finding probabilities of five or fewer successes in nine trials, no more than 11 and no less than 6 successes in 16 trials, probabilities of all successs or failures in multiple trials, and probabilities of three or more successs or failures in a binomial distribution.

Typology: Study notes

Pre 2010

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STAT 301 TA : Lisa Chung [email protected]
DISCUSSION 5
(Oct.11. 2004)
Binomial Table
Example 1. Using Binomail Table, find the probability of
a. Five or fewer successes in 9 trials then p=.7
b. No more than 11 and no less than 6 successes in 16 trials when p=.6
Example 2. Consider four Bernoulli trials with success probability p=.7 in each trial. Find the proba-
bility that
a. All four trials result in successes.
b. There is at least one success.
Example 3. For the binomial distribution with n=4 and p=.25, find the probability of
a. Three or more successes
b. Two or more failures
Example 4. If in three Bernoulli trials P(all three are successes) = .027, what is the probability that all
three are failures?
Example 5. Let Y be a binomial random variable with n = 10 and µ= 1.0. Then P(Y > 2) ?
Off. Hour: W 1:00-3:00 p.m. 1 1275A MSC, 262-1577

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STAT 301 TA : Lisa Chung [email protected]

DISCUSSION 5

(Oct.11. 2004)

Binomial Table

Example 1. Using Binomail Table, find the probability of a. Five or fewer successes in 9 trials then p=.

b. No more than 11 and no less than 6 successes in 16 trials when p=.

Example 2. Consider four Bernoulli trials with success probability p=.7 in each trial. Find the proba- bility that a. All four trials result in successes.

b. There is at least one success.

Example 3. For the binomial distribution with n=4 and p=.25, find the probability of a. Three or more successes

b. Two or more failures

Example 4. If in three Bernoulli trials P(all three are successes) = .027, what is the probability that all three are failures?

Example 5. Let Y be a binomial random variable with n = 10 and μ = 1.0. Then P (Y > 2)?

Off. Hour: W 1:00-3:00 p.m. 1 1275A MSC, 262-