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12.5 Probability of Independent and Dependent Events
AND/THEN – decide if you are dealing with multiple events that DO depend on each other OR multiple events
that DO NOT depend on each other.
Independent Events – the outcome of an event has NO effect on the outcome of another event.
Probability of Independent Events = P ( A and B) =
Ex: Draw one card. Replace the card in the deck. Draw a second card.
Find the probability of drawing king first and an ace second.
Dependent Events – the outcome of an event IS affected by the outcome of another event.
Probability of Dependent Events = P ( A and B)
Ex: Draw one card. DO NOT replace the card in the deck. Draw a second card.
Find the probability of drawing king first and an ace second.
Example 1: A die is rolled twice. Find the probability of an odd on the first roll and an odd on the second roll.
Example 2: For a fundraiser, a class sells 150 raffle tickets for a mall gift certificate and 200 raffle tickets for a
booklet of movie passes. You buy 5 raffle tickets for each prize. What is the probability that you win both
prizes?
Example 3: Find the probability of drawing the given cards from a standard deck of 52 cards. A) First find the
probability if you replace the card, then B) Find the probability if you DO NOT replace the card.
a) A club, then a spade
b) A heart, then a club, then a heart
c) A king or queen, then any face card
d) A diamond, then a red card
Example 4: A jar contains 3 red gumballs, 5 green gumballs, and 6 orange gumballs. Find the probability that
two red gumballs are chosen if no gumballs are replaced.
Homework: p. 734-736 #12-23 all
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