# Probabilities of Compound Events  Probability of Two Independent Events  If two events, A and B are independent, then the probability of both events.

## Presentation on theme: "Probabilities of Compound Events  Probability of Two Independent Events  If two events, A and B are independent, then the probability of both events."— Presentation transcript:

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?

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