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Question

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


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Solution

Step 1 : The content we have and the formula for the probability

Number of red balls =5

Number of blue balls =x

PA=number of outcome favourable to Atotal number of possible outcome

or

PA=nAnS

where,

  • PA is probability of an event 'A'
  • nA is the favorable outcome of the event 'A'
  • nS is total number of possible outcome in a sample space

Step 2: Probability of blue and red balls

Let A be the event of getting blue balls, nA and n(S) be the number of blue balls and total balls available accordingly.

B be the event of getting red balls, nB and nS be the number of red balls and total balls available accordingly.

PA=nAnS

Total number of balls=5+x

PA=x5+x

P(B)=n(B)n(S)

PB=55+x

Step 3: Applying the condition

Probability of drawing blue ball according to the condition=2×PB

x5+x=255+x

x=2×5=10

Hence,the number of blue balls in the bag is 10.


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