Transcript 13.1 Permutations and Combinations

13.4 Probabilities of
Compound Events
• Find the probability of independent and
dependent events.
• Identify mutually exclusive events.
• Find the probability of mutually exclusive
and inclusive 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)
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)
1) When three dice are rolled, what is the probability that the first two
show a 5 and the third shows an even number?
2) At a picnic, Julio reaches into an ice-filled cooler containing 8
regular soft drinks and 5 diet soft drinks. He removes a can, then
decides he is not really thirsty, and puts it back. What is the
probability that Julio and the next person to reach into the cooler
both randomly select a regular soft drink?
3) Three cards are drawn from a standard deck of cards without
replacement. Find the probability of drawing a diamond, a club,
and another diamond in that order.
1. The host of a game show is drawing chips from a bag to determine
the prizes for which contestants will play. Of the 10 chips in the
bag, 6 show television, 3 show vacation, and 1 shows car. If the
host draws the chips at random and does not replace them,
a) Find the probability that he draws a vacation, then a car.
b) Find the probability that the host draws two televisions.
2. In a state lottery game, each of three cages contains 10 balls. The
balls are each labeled with one of the digits 0-9. What is the
probability that the first two balls drawn will be even and that the
third will be prime?
Probability of Mutually Exclusive Events
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)
Probability of Inclusive Events
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
occurring.
𝑃 𝐴 𝑜𝑟𝐵 = 𝑃 𝐴 + 𝑃 𝐵 − 𝑃(𝐴 𝑎𝑛𝑑 𝐵)
1) Keisha has a stack of 8 baseball cards, 5 basketball cards, and 6
soccer cards. If she selects a card at random from the stack, what
is the probability that it is a baseball or a soccer card?
2) The Cougar basketball team can send 5 players to a basketball
clinic. Six guards and 5 forwards would like to attend the clinic. If
the players are selected at random, what is the probability that at
least 3 of the players selected to attend the clinic will be forwards?
1) Suppose that of 1400 students, 550 take Spanish, 700 take biology,
and 400 take both Spanish and biology. What is the probability that
a student selected at random takes Spanish or biology?
2) Sylvia has a stack of playing cards consisting of 10 hearts, 8 spades,
and 7 clubs. If she selects a card at random from this stack, what is
the probability that it is a heart or a club?
1) In a bingo game, balls numbered 1 to 75 are placed in a bin. Balls are
randomly drawn and not replaced. Find each probability for the first 5
balls drawn.
a) P(selecting 5 even numbers)
b) P(selecting 5 two digit numbers)
c) P(5 odd numbers or 5 multiplies of 4)
d) P(5 even numbers or 5 numbers less than 30)