Probability

Question

A bag contains 12 red marbles,5 yellow marbles, and 15 green marbles. How many marbles must be added to the 32 marbles already in the bag so that the probability of randomly drawing a red marble is 3/5?

Answer 1

The probability of initially drawing a red marble is 12/32 =3/8,

 

This is less than 3/5, hence X red marbles must be added to the bag to increase its probability

 

If the probability of drawing a red is to be 3/5, then the probability of drawing either yellow or green must be 2/5

 

seeing that there are 5+15 green or red marbles in the bag

 

then equating probabilities 2/5 = 20/X, 

 

X therefore = 50 marbles, hence 50-32 = 18 red marbles must be added to the bag.

 

Checking; probability of drawing a red = (12+18)/(32+18) = 30/50 = 3/5

Answer 2

r=# red marbles to be added

(12+r)/(32+r)=3/5

5(12+r)=3(32+r)

60+5r=96+3r

5r-3r=96-60

2r=36

r=36/2

r=18 red marbles must be added

 

(12+18)/(32+18)=30/50=3/5