Chapter 11 Probability Worksheet Page 11
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PROBABILITY (Chapter 11)
b
Use your grid to determine the probability of getting:
i
ii
iii
a Queen
the Jack of hearts
a spade
a red 7
iv
a picture card
v
vi
a diamond or a club
a Queen and a 3:
vii
viii
a King or a heart
The medical records for a class of 28 children show whether they had previously had
13
measles or mumps. The records show 22 have had measles, 13 have had measles and
mumps, and 27 have had measles or mumps. If one child from the class is selected at
random, determine the probability that he or she has had:
a
measles
b
mumps but not measles
c
neither mumps nor measles.
E
COMPOUND EVENTS
We have previously used two-dimensional grids to represent sample spaces and hence find
answers to certain probability problems.
Consider again a simple example of tossing a coin and rolling a die simultaneously.
coin
To determine the probability of getting a head and a ‘5’,
we can illustrate the sample space on the two-dimensional
We can see that there are 12 possible
T
grid shown.
outcomes but only one with the property that we want, so
H
1
the answer is
.
12
die
1
2
3
4
5
6
1
1
However, notice that P(a head) =
, P(a ‘5’) =
2
6
1
1
1
£
=
and
:
2
6
12
This suggests that P(a head and a ‘5’) = P(a head) £ P(a ‘5’),
i.e., we multiply the separate probabilities.
It seems that if A and B are two events for which the occurrence of each one does not affect
the occurence of the other, then P(A and B) = P(A) £ P(B).
The two events ‘getting a head’ and ‘rolling a 5’ are events with this property, as the occurrence
or non-occurrence of either one of them cannot affect the occurence of the other. We say
they are independent.
If two events A and B are independent then P(A and B) = P(A) £ P(B).
Example 7
Self Tutor
A coin is tossed and a die rolled simultaneously. Find the
probability that a tail and a ‘2’ result.
‘Getting a tail’ and ‘rolling a 2’ are independent events.
)
P (a tail and a ‘2’) = P(a tail) £ P(a ‘2’)
1
1
=
£
2
6
1
=
12
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