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MATH 1P98: Binomial Probabilities

Mathematics and Statistics
Course Code
Dot Miners

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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
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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