2.A bag contains 10 discs of which 5 are red, 3 are blue and 2 are green. A disc is to be taken from the bag at random. (a)Calculate the probability that the disc will be red. On a second occasion, from the bag of 10 discs, 2 discs are to be taken at random. Calculate the probability that the discs will be (b) of the same colour (c) of different colour. on a third occasion, from the bag of 10 discs. 3 discs are to be taken at random. Calculate the probability that the discs will be (d) all red (e) of the same colour (1) red, blue, green in that order (g) red, blue, green in any order.
Answers
Answer:
P
r
=
13
18
Explanation:
The first thing to do is to convert these possibilities into a tree diagram, like the one below which I did in Word:
enter image source here
Where
R
equals red disc,
Y
equals yellow disc and
P
equals purple disc.
To find the probability of 2 discs being chosen that are different colours, we simply subtract the probabilities that both colours are the same from 1. This means we must find
P
r
(
R
,
R
)
,
(
Y
,
Y
)
and
(
P
,
P
)
.
From the diagram, we see
P
r
(
R
,
R
)
=
4
9
⋅
3
8
P
r
(
R
,
R
)
=
12
72
=
1
6
.
We also see
P
r
(
Y
,
Y
)
=
3
9
⋅
2
8
P
r
(
Y
,
Y
)
=
6
72
=
1
12
and
P
r
(
P
,
P
)
=
2
9
⋅
1
8
P
r
(
P
,
P
)
=
2
72
=
1
36
.
Next we add all these probabilites together to get
1
6
+
1
12
+
1
36
=
5
18
.
Since the probabilities of getting the same colour are complementary to getting different colours, we can use the rule
P
r
(
A
'
)
=
1
−
P
r
(
A
)
, where
A
'
is the complementary group of
A
.
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