There are 5 red balls, 3 white balls, and 2 yellow balls in the box. If you don't put back two balls are drawn, find the probability that both balls are yellow.
Question
There are 5 red balls, 3 white balls, and 2 yellow balls in the box. If you don't put back two balls are drawn, find the probability that both balls are yellow.
Solution
The probability of drawing two yellow balls without replacement can be calculated by multiplying the probability of drawing the first yellow ball by the probability of drawing the second yellow ball.
The probability of drawing the first yellow ball is 2 out of 10 (since there are 2 yellow balls and 10 total balls). So, P(Yellow1) = 2/10 = 0.2.
After drawing the first yellow ball, there is now 1 yellow ball left and 9 total balls. So, the probability of drawing the second yellow ball is 1 out of 9. So, P(Yellow2) = 1/9.
The probability of both events happening is the product of their individual probabilities. So, P(Yellow1 and Yellow2) = P(Yellow1) * P(Yellow2) = 0.2 * 1/9 = 0.0222 (rounded to four decimal places).
So, the probability that both balls are yellow is 0.0222.
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