25 pieces of fruit are in a bowl. 14 of them are apples. a piece of fruit is randomly drawn from the bowl…
25 pieces of fruit are in a bowl. 14 of them are apples. a piece of fruit is randomly drawn from the bowl. without replacing the first one, a second piece is drawn. what is the probability that both of the pieces of fruit drawn are apples? round your answer to the nearest hundredth.
Answer
Explanation:
Step1: Calculate first - draw probability
The probability of drawing an apple on the first draw is the number of apples divided by the total number of fruits. There are 14 apples and 25 total fruits, so the probability $P_1=\frac{14}{25}$.
Step2: Calculate second - draw probability
After drawing one apple on the first draw, there are 13 apples left and 24 total fruits left. So the probability of drawing an apple on the second draw given that an apple was drawn on the first draw is $P_2 = \frac{13}{24}$.
Step3: Calculate joint - probability
The probability that both events occur (both fruits are apples) is the product of the probabilities of each event. So $P = P_1\times P_2=\frac{14}{25}\times\frac{13}{24}=\frac{182}{600}=\frac{91}{300}\approx0.30$.
Answer:
0.30