A jar of 70 candies has the following colors: 28 orange, 7 white, 14 brown, and 21 yellow.
What is the probability of randomly drawing a yellow and then a brown candy without replacing the yellow one?
The probability of drawing a yellow candy on the first draw is 21/70. Since we do not replace the yellow candy, there are now 69 candies in the jar. The probability of drawing a brown candy on the second draw is 14/69.
To find the probability of both events occurring, we multiply their probabilities: (21/70) * (14/69) = 294/4830.
Simplifying the fraction gives us a final probability of 7/115.
To find the probability of drawing a yellow and then a brown candy without replacing the yellow one, we'll use the concept of conditional probability.
The probability of drawing a yellow candy is 21 out of 70, as there are 21 yellow candies out of the total of 70 candies.
After drawing a yellow candy, there will be 69 candies left in the jar. However, since we don't replace the yellow candy, there will be 20 yellow candies left out of the 69 remaining candies.
The probability of drawing a brown candy from the remaining 69 candies is 14 out of 69, as there are 14 brown candies out of the remaining 69 candies.
Therefore, the probability of randomly drawing a yellow and then a brown candy without replacing the yellow one is:
(21/70) * (14/69) = 0.0897 or approximately 8.97%