Question

40 bugs are in a bucket. 17 of them are ladybugs. a bug is randomly drawn from the bucket. without replacing the first one, a second bug is drawn. what is the probability that both of the bugs drawn are ladybugs? round your answer to the nearest hundredth.

Explanation:

Step1: Calculate first - draw probability

The probability of drawing a ladybug on the first draw is the number of ladybugs divided by the total number of bugs. There are 17 ladybugs and 40 bugs in total, so the probability $P_1=\frac{17}{40}$.

Step2: Calculate second - draw probability

After the first ladybug is drawn without replacement, there are 16 ladybugs left and 39 bugs left. So the probability of drawing a ladybug on the second draw given that a ladybug was drawn on the first draw is $P_2 = \frac{16}{39}$.

Step3: Calculate the joint - probability

The probability that both bugs are ladybugs is the product of the probabilities of each draw. So $P = P_1\times P_2=\frac{17}{40}\times\frac{16}{39}=\frac{17\times16}{40\times39}=\frac{272}{1560}\approx0.17$

Answer:

0.17