from a bag containing 6 white balls, 3 black balls and 13 red balls, two balls are drawn at random. what is the probability that they are both red?
test
To find the probability that both balls drawn are red, we first need to determine the total number of possible outcomes and the number of favorable outcomes.
The total number of balls in the bag is 6 white + 3 black + 13 red = 22 balls.
When the first ball is drawn, the total number of balls is reduced by 1, so there are 21 balls remaining.
The probability of drawing a red ball on the first draw is 13 red balls / 21 total balls.
After the first ball is drawn and it's red, there are 12 red balls left out of the remaining 20 balls.
The probability of drawing a red ball on the second draw, given that the first ball was red, is 12 red balls / 20 total balls.
To find the probability of both events happening, we multiply the probabilities of each event together.
Probability of drawing a red ball on the first draw: 13/21
Probability of drawing a red ball on the second draw, given that the first ball was red: 12/20
Probability that both balls drawn are red = (13/21) * (12/20) = 0.2286 or 22.86%
Therefore, the probability that both balls drawn are red is approximately 0.2286 or 22.86%.