Chapter 11 Probability Worksheet Page 13
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PROBABILITY (Chapter 11)
DEPENDENT EVENTS
Suppose a cup contains 4 red and 2 green marbles. One marble is randomly chosen, its colour
is noted, and it is then put aside. A second marble is then randomly selected. What is the
chance that it is red?
3 reds remaining
3
If the first marble was red, P(second is red) =
5
5 to choose from
4 reds remaining
4
If the first marble was green, P(second is red) =
5
5 to choose from
So, the probability of the second marble being red depends on what colour the first marble
was. We therefore have dependent events.
Two or more events are dependent if they are not independent.
Dependent events are events for which the occurrence of one of the
events does affect the occurrence of the other event.
For compound events which are dependent, a similar product rule applies as to that for
independent events:
If A and B are dependent events then
P(A then B) = P(A) £ P(B given that A has occurred).
Example 9
Self Tutor
A box contains 4 blue and 3 yellow buttons of the same size. Two buttons are randomly
selected from the box without replacement. Find the probability that:
a
both are yellow
b
the first is yellow and the second is blue.
a
P(both are yellow)
= P(first is yellow and second is yellow)
= P(first is yellow) £ P(second is yellow given that the first is yellow)
2 yellows remaining
3
2
=
£
7
6
6 to choose from
1
=
7
b
P(first is Y and second is B)
= P(first is Y) £ P(second is B given that the first is Y)
4 blues remaining
3
4
=
£
7
6
6 to choose from
2
=
7
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