Download Probabilities of Compound Events

Probabilities of Compound Events
 Probability
of Two Independent Events
 If
two events, A and B are independent,
then the probability of both events
occurring is the product of each individual
probability.
 P(A and
B) = P(A) * P(B)
Probabilities of Compound Events
 Find
the probability of drawing a face card,
replacing the card and then drawing an
ace using a standard deck of playing cards
 P(A)=
12/52
 P(B)= 4/52
 P(A and B) = 12/52 * 4/52 = 3/169
Probabilities of Compound Events

In a survey it was determined that 7 out of 10
shoppers do not use coupons and 3 out of 8
shoppers only buy items on sale. What is the
probability that a random shopper will use a
coupon and buy a item on sale. (It has been
determined that these two situations are independent.)

P(A) = 1 - 7/10 = 3/10
 P(B) = 3/8
 P(A and B) = 3/10 * 3/8 = 9/80
Probabilities of Compound Events
 Probability
of Two Dependent Events
 If two events, A and B, are dependent,
then the probability of both events
occurring is the product of each individual
probability.
 P(A and
B) = P(A) * P(B following A)
Probabilities of Compound Events
 In
a bag there are 4 red, 6 green and 3
blue candies. Bob will pick 3 candies
randomly from the bag (no replacement).
 Independent or dependent?
 What is the probability that Bob drew all
blue candies?
 P(A, then B, then C)
 3/13 * 2/12 * 1/11 = 1/286
Probabilities of Compound Events
 Probability

of Mutually Exclusive Events
Mutually exclusive: When two events cannot
happen at the same time
 If
two events, A and B are mutually
exclusive, then the probability that either A
or B occurs is the sum of their probabilities
 P(A or
B) = P(A) + P(B)
Probabilities of Compound Events
 Betty
has 6 pennies, 4 nickels and 5 dimes
in her pocket. If Betty takes one coin out
of her pocket, what is the probability that it
is a nickel or a dime?
 P(A) = 4/15
 P(B) = 5/15
 P(A or
B) = 4/15 + 5/15 = 9/15 = 3/5
Probabilities of Compound Events
 Probability

of Inclusive Events
Mutually Inclusive: When two events can
happen at the same time
 If
Two events, A and B are inclusive, then
the probability that either A or B occurs is
the sum of their probabilities decreased by
the probability of both events occurring.
 P(A or
B) = P(A) + P(B) – P(A and B)
Probabilities of Compound Events
 In
a particular group of hospital patients,
the probability of having high blood
pressure is 3/8, the probability of having
arteriosclerosis is 5/12, and the probability
of having both is ¼.
 Mutually exclusive or inclusive?
 What is the probability that a patient has
either HBP or arteriosclerosis?
Probabilities of Compound Events
 There
are 6 children in an art class, 4 girls
and 2 boys. Four children will be chosen
at random to act as greeters for an art
exhibit. What is the probability that at
least 3 girls will be selected?