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?

Question

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?

radar · Answer

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.

radar · Answer

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!

radar · Answer

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.

radar · Answer

Any questions on this solution?