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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'

1 Answer

4 votes

Answer:

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.

User Luckyrat
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