Question

A bag contains 5 red balls and some blue balls. If the probability of drawing a blue ball is double that of a red ball determine the number of blue balls in the bag?

Answer 1

Let the number of blue balls be x and the probability of drawing a red ball be P(r) and that of drawing blue ball be P(b).

Since,
P(r)+P(b)=1

P(r)+2P(r)=1

3P(r)=1

P(r)=1/3

Thus the probability of drawing red ball is 1/3.

As Probability= Favourable outcomes/total outcomes.

Therefore,

$\frac{5}{x + 5} = \frac{1}{3} \\ 15 = x + 5 \\ x = 10$
The number of blue balls are 10.

Answer 2

Answer:

Let there be x blue balls in the bag.

Total no. Of blue balls=(5+x)

Now,

p1=probability of drawing a blue ball=x/5+x

p2=probability of drawing a red ball=5/5+x

It is given that

p1 =2p2

x/5+x=2×5/5+x

→x/5+x=10/5+x

→ x=10

Hence,there are 10 balls in the bag