Probability And Statistics Worksheets Page 18
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42When the outcome of one event is affected by the outcome of
Check
another, the events are said to be dependent.
Understanding
Are these events
E x a m p l e 2
independent or
dependent?
SPORTS
Six teams—the Panthers, Tigers, Lions, Bears, Cheetahs,
1. tossing a coin twice
and Elephants—are in the lottery round for this year’s draft picks.
2. picking two marbles
The name of each team is written on a card and placed in a box.
from a bag without
replacing the first one
To determine who gets the first lottery pick, one card will be drawn
at random and not replaced. Then a second card will be drawn at
3. choosing a captain and
then choosing a co-
random to determine the second pick. What is the probability that
captain
the Bears get the first draft choice and the Lions get the second
4. rolling three dice
draft choice?
Solution
Because the first card is not replaced, the sample space for the second drawing
has been changed. The second event is dependent on the first event.
Probability of first event
number of Bears cards
1
P(Bears)
total number of cards
6
Probability of second event
number of Lions cards
1
P(Lions, after Bears)
new total number of cards
5
Multiply the probabilities.
1
1
P(Lions, after Bears)
6
5
1
3
0
1
The probability of drawing the Bears first and the Lions second is
.
3
0
E x a m p l e 3
A bag contains 3 green marbles, 2 red marbles, 4 yellow marbles, and
1 black marble. Two are taken at random from the bag without
replacement. Find P(green, then green).
Solution
number of green marbles
3
P(first green marble)
total number of marbles
1
0
number of green marbles
3
1
2
P(second green marble)
total number of marbles
1
0
1
9
Multiply the probabilities.
3
2
P(green, then green)
1
0
9
6
1
9
0
1
5
1
The probability of picking green, then green, is
.
1
5
397
Lesson 9-4 Independent and Dependent Events
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