Question

A bag contains, red, blue and yellow balls

the probability of picking a red ball is 1/3
the probability of picking a blue ball is 1/5


a.) Work out the probability of picking a yellow ball

b.) There are 10 red balls
How many balls are there in total

c.) Grace adds 10 balls to the bag so that:
P(red) = 1/4 and P(blue) = 2/5
How many of each color does she add

Please space out your answer and label 'a' 'b' and 'c'

Answer 1

a)
`(7)/(15)`

b) There are 30 balls

c) Number of blue balls added = 10, number of red balls added = 0 and number of yellow balls added = 0

Explanation:

a) Sub of the probabilities is always 1.

Therefore,

p(red) + p(blue) + p(yellow) = 1

`(1)/(3) +(1)/(5) +p(yellow) = 1`

`p(yellow) = 1-(1)/(5) -(1)/(3)`

`= 1-(8)/(15)`

`=(7)/(15)`

b) p(red ball) =
`(n(E))/(n(S)) =(1)/(3)`

But, it is given that n(E) = 10

Therefore,
`(10)/(n(S)) =(1)/(3)`

n(S) = 30

Hence, there are 30 balls in total

c) From b), there are 10 red balls.

Now, p(blue ball) =
`(n(E))/(n(S)) =(1)/(5)`

Since, n(S) = 30,

`(n(E))/(30) =(1)/(5)`

n(E) = 6

There are 6 blue balls and

the number of yellow balls = 30 - (10 + 6) = 14

After adding 10 balls, n(S) = 40

p(blue ball) =
`(2)/(5)`

`n(E) = (2)/(5) (40)`

= 16

But, number of blue balls before addition = 6.

Hence, all the added balls are blue.