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Transcript
230
PROBABILITY (Chapter 10)
EXERCISE 10F
1 Two coins are tossed simultaneously. Use a 2-dimensional grid to illustrate the sample
space and hence determine the probability of getting:
a two tails
b a head and a tail
c at least one tail.
2 A coin and a die are tossed simultaneously. Draw a 2-dimensional grid to illustrate the
sample space. Determine the probability of getting:
a a tail and a 6
c neither a 2 nor a 6
e a head and an odd number
b a tail or a 6
d neither a tail nor a 5
f a head or an odd number.
3 Draw a 2-dimensional grid to illustrate the sample space when an ordinary die is tossed
and a triangular spinner labelled A, B and C is spun simultaneously. Hence, determine
the probability of getting:
a B and 5
c a non-B and a multiple of 3.
b A and a prime number
4 A pair of dice is rolled. The 36 different
possible ‘pair of dice’ results are illustrated
on the 2-dimensional grid alongside.
Use the grid to determine the probability of
getting:
a two 3s
c a 5 or a 6
e exactly one 6
die 2
6
5
4
3
b a 5 and a 6
d at least one 6
f no sixes
2
1
1
g a sum of 7
h a sum of 7 or 11
i a sum greater than 8
2
3
4
5
die 1
6
j a sum of no more than 8.
G
COMPOUND EVENTS
Consider the following problem:
Box X contains 2 blue and 2 green balls. Box Y
contains 3 red and 1 white ball. A ball is randomly
selected from each of the boxes. Determine the
probability of getting a blue ball from X and a red
ball from Y.
B
R
R
= 38 :
R
box X
95
50
75
B
25
0
5
95
100
50
75
25
0
5
95
50
75
25
0
5
95
100
50
75
25
0
5
100
magenta
R W
Y
box Y
In the investigation that follows, we will seek a
quicker, easier way to find this probability.
cyan
R
W
yellow
Y:\HAESE\IB_MYP4\IB_MYP4_10\230IB_MYP4_10.CDR Tuesday, 18 March 2008 1:32:44 PM PETERDELL
100
6
16
R
G G
X
By illustrating the sample space on a twodimensional grid as shown alongside, we see that
6 of the 16 possibilities are blue from X and red
from Y. Since each outcome is equally likely,
P(blue from X and red from Y) =
B
black
B
G
G
IB MYP_4