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given Question -
A bag contains 15 balls of which x are blue and the remaining are red. If the number of red balls are increased by 5, the probability of drawing the red balls doubles. Find
1. P(red ball)
2. P(blue ball)
3. P(blue ball if 5 extra balls are actually added)
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Answer:
given,
no. of blue balls = x
no. of red balls =(15-x)
total balls = 15
Probability of drawing Red ball = (15-x)/15 (A)
after adding 5 red balls,
no. of blue balls = x
no. of red balls =(15-x) + 5 = 20 - x
total balls = 15 + 5 = 20
Probability of drawing Red ball = (20-x)/20 (B)
given that (B) = 2(A)
hence,
(20-x)/20 = 2 ×(15-x)/15
=> 3 × (20-x) = 8 ×(15-x)
=> 60 - 3x = 120 - 8x
5x = 60
x = 12
Hence,
TOTAL NUMBER OF BLUE BALLS = 12
TOTAL NUMBER OF RED BALLS = 15 - 12 = 3
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ANSWER ------>
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i. P(red ball) = 3/15 = 1/5
ii. P(blue ball) = 12/15 = 4/5
iii. P(blue ball if 5 extra balls are actually added) = 12/(15+5) = 12/20 = 3/5
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