jack has 4 red pencils, 3 green, 2 blue and purple. jack wants there to be a 1/2 chance that he will pick a purple pencil. how many more do you have to add so there will be a chance of1/2?
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Total number of pencils that Jack presently has is the sum of 4 red+3 green+2blue+2purple=11. So jack now has a 2 out of 11 probability of purple.
Let x = the additional purple pencils needed then from the information given:
2+x=1/2(22+x) The 1/2 is the required chance for purple.
Multiplying each side by 2 gives: 4+2x=22 + x. Subtracting x from both sides
result in: 4+x=22 subtracting 4 from both sides gives: x=18. Check it out!
Proof: With 18 additional purple pencils, Jack has a total of 40 pencils. 20 of them are purple. sure is a lot of pencils but he does have a 50-50 chance of choosing a purple one.