This

**preview**shows half of the first page. to view the full**2 pages of the document.**Binomial Probabilities

1) Fixed number of trials

2) The trials are independent (outcome from one doesn’t affect next)

3) Each trial has two outcomes; s = success, f = failure

4) Each trial has an equal likelihood of success

5) The problem is to find the probability of r successes from n trials

Ex: left handed people in a group

n = 55 people

r = 10

p= 0.1

q = 0.9

AND cases: find probabilities separately and add together (ex: picking colored balls out of bag –

make sure to account for denominator change, ie ball is taken out)

OR cases: Sum of all probabilities minus probability of two events together (Ex: chocolate or

caramel or both minus overlap)

MUTUALLY EXCLUSIVE cases: two events cannot happen together (ex: rolling a number on a

die)

P(Math) = 70% P(English) = 80% P(Math and English) = 55%

P(Math or English) = 0.7 + 0.8 – 0.55

= 95%

P(r) = nCr*pr*qn-r

P (A or B) = P(A) + P(B) – P(A and B) Non-mutually

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