a bag of 100 blue and purple marbles has three times as many blue marbles as purple marbles.if purple marbles are added to the bag until the number of purple marbles in the bag is double the original amount,what is the probability of taking out a blue marble and then choosing another blue marble?
Answers
Given : A bag of 100 blue and purple marbles has three times as many blue marbles as purple marbles.
Purple marbles are added to the bag until the number of purple marbles in the bag is double the original amount,
To Find : what is the probability of taking out a blue marble and then choosing another blue marble?
Solution:
three times as many blue marbles as purple marbles
purple marbles = A
blue marbles = 3A
Total Marbles = A + 3A = 4A
Total marbles = 100
4A = 100
=> A = 25
purple marbles = 25
blue marbles = 75
purple marbles are added to the bag until the number of purple marbles in the bag is double the original amount
=> 25 purple marbles are added
purple marbles now = 25 + 25 = 50
purple marbles = 50
blue marbles = 75
Total Marbles = 125
probability of taking out a blue marble and then choosing another blue marble = (75/125)(50/124)
= (3/5)(50/124)
= 30/124
= 15/62
probability of taking out a blue marble and then choosing another blue marble = 15/62
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