Mathematics Department
Yea8
Term 2 W1
Homework
Name…………………
Week …………………
Class…………………
1 A spinner has sectors in four colours, red, blue, green and yellow.
1 P(red) = 0.15
P(blue) = 0.21
Green and yellow are equally likely.
Work out the probability of landing on
a green
P(green)=1-0.36 =0.64/3 = 0.32
b neither blue nor yellow.
[1]
P(green or yellow) ' = 0.21+0.32= 0.53 = 1 - 0.53= 0.47
[1]
2 There are 16 lettered balls in a bag. Five balls have letter M, two balls have letter A,
three balls have letter T and the rest of the balls have letter H.
A ball is taken at random. Find the probability that the ball has the letter
a M or A
b H
P(A or M)= 5+2=7= 7/16
M=5
A=2
T=3
H=6
[1]
P(H)=6/16
[1]
3 Arun is late for work. Sofia is late for work.
a Describe a situation where these are not independent events.
Sofia can be late for work for a different reason than Arun
[1]
b Describe a situation where these are independent events.
that they are married and go to work with each other.
[1]
4 There are four balls in a bag. The balls are numbered 1, 2, 3 and 4. A ball is taken out
of the bag at random. Here are three events:
X: an even number
Y: 1 or 2
Z: less than 4
a Show that X and Y are independent events.
P(X) ' =2/4
P(Y) =2/4
[2]
b Show that X and Z are not independent.
P(Z)=3/4
P(X)' = 2/4
[2]
5
A spinner is divided into 20 equally likely sectors. Each sector is gold, silver or bronze.
5/20
P(gold) =
1
2
and P(silver) = .
5
4
8/20
Work out the probability that the sector is
a not silver
b bronze.
P(silver)'=1- 5/20 =15/20
P(Bronze)=5/20 + 8/20=13/20 = 1-13/20 = 7/20
[1]
[1]
6 Here are two spinners with black (B) and white (W) sectors:
On the first spinner P(black) =
3
.
4
On the second spinner P(black) =
1
.
3
a Complete this tree diagram. Put probabilities on the branches.
2/3
1/3
1/4
2/3
[2]
b Work out the probability that
i both spinners land on black
3/12
[1]
ii both spinners land on the same colour.
5/12
[1]
7 Zara rolls a fair dice twice. She is trying to throw 6s.
a Complete this tree diagram. Put probabilities on the branches.
1/6
1/6
5/6
1/6
5/6
5/6
[2]
b Work out the probability of rolling at least one 6 in two rolls.
10/36
[2]