A bag contains 8 red balls and some white balls. If the probability of drawing a white ball is half

Explanation

Let w represent the number of white balls. Probability of white equals w divided by total, and probability of red equals 8 divided by total. We know white probability is half of red probability, so w divided by total equals half times 8 divided by total.

This simplifies to w equals 4 white balls. Total balls equals 8 plus 4 equals 12 balls. Probability of red is eight-twelfths and probability of white is four-twelfths.

For drawing red then white without replacement: eight-twelfths × four-elevenths equals thirty-two over one hundred thirty-two equals eight over thirty-three. We multiply by four-elevenths because after removing one red ball, only 11 balls remain.