Probabilities of Compound Events

1
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)

2
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

3
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

4
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)

5
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

6
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)

7
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

8
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)

9
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?

10
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?