An urn contains two white balls and three black balls. The balls are drawn from the urn oneby one and placed on a surface in the drawn order. Find the probability that they are drawn in theorder white, black, black, white, black?
Question
An urn contains two white balls and three black balls. The balls are drawn from the urn oneby one and placed on a surface in the drawn order. Find the probability that they are drawn in theorder white, black, black, white, black?
Solution
To solve this problem, we need to understand that the drawing of balls is a dependent event, meaning the outcome of the first draw affects the outcome of the subsequent draws.
Step 1: Calculate the probability of drawing the first white ball. There are 2 white balls and 5 total balls, so the probability is 2/5.
Step 2: After the first white ball is drawn, there is now 1 white ball and 4 total balls left. So, the probability of drawing a black ball next is 3/4.
Step 3: After the black ball is drawn, there are now 2 black balls and 3 total balls left. So, the probability of drawing another black ball is 2/3.
Step 4: After the second black ball is drawn, there is now 1 white ball and 2 total balls left. So, the probability of drawing a white ball is 1/2.
Step 5: After the white ball is drawn, there is now 1 black ball and 1 total ball left. So, the probability of drawing a black ball is 1/1 or 100%.
Step 6: Multiply all these probabilities together to get the final probability.
So, the probability that the balls are drawn in the order white, black, black, white, black is (2/5) * (3/4) * (2/3) * (1/2) * (1/1) = 0.1 or 10%.
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