Transcript Lesson 12-4: Multiplying Probabilities

Multiplying Probabilities
Advanced Math Topics
Probability of Two Independent
Events
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If two events A and B are independent
then the probability of both events
occurring is P(A and B) = P(A) ∙ P(B)

This can be applied to any number of
independent events!
Example 1

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 in back. What is the probability that Julio and
the next person to reach into the cooler both randomly
select a regular soft drink?
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Ask yourself are these events independent? YES the outcome of
the second person getting a drink is not affected by Julio’s
selection
Make a plan, 13 cans and 8 are regular soft drinks so the
probability of each person getting a regular soft drink is 8/13
Solve, P(both regular soft drinks) = P(regular) ∙ P(regular)
8/13 ∙
8/13
= 38%
Example 2

Gerardo has 9 dimes and 7 pennies in his pocket. He
randomly selects one coin, looks at it, and replaces it.
He then randomly selects another coin. What is the
probability that both coins he selects are dimes?
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Ask yourself are these events independent? YES, the outcome of
the first selection doesn’t affect the second selection
Make a plan, 16 coins and 9 are dimes so the probability of
picking a dime is 9/16
Solve, P(Both dimes) = P(dime) ∙ P(dime)
9/16 ∙ 9/16
81/256
Example 3

In a board game, three dice are rolled to
determine the number of moves for the
players. What is the probability that the
first die shows a 6, the second die shows
a 6, and the third die does not?
Example 4

When three dice are rolled, what is the
probability that the first two show a 5 and
the third shows an even number?
Probability of Dependent Events

If two events A and B are dependent, then
the probability of both events occurring is
P(A and B) = P(A) ∙ P(B following A)
Back to Example 1 Part B
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What is the probability that both people select a
regular soft drink if Julio does not put his back in
the cooler?
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Ask are these two events dependent, YES, the
outcome of the second person choosing a drink is
affected by Julio not putting his back
Make a plan, Julio has a 8/13 probability while the
second person now has 7/12
Solve, 8/13 ∙ 7/12 = 56/156 = 14/39
= 36%
Example 5

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?
Example 6
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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, find the probability that
he draws a vacation, then a car.
Example 6 part b
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Use the information above. What is the
probability that the host draws two
televisions?
Example 7

The host of a game show is drawing ships
from a bag to determine the prizes for
which contestants will play. Of the 20
chips, of which 11 say computer, 8 say
trip, and 1 says truck. If chips are drawn
at random and without replacement, find
the probability of drawing a computer,
then a truck.
Example 8
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Three cards are drawn from a standard
deck of cards without replacement. Find
the probability of drawing a heart, another
heart, and a spade in that order.
Example 9
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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.
Example 10
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Find the probability of drawing three cards
of the same suit.