Question

35 birds are in a cage. 14 of them are robins. a randomly selected bird is taken from the cage. without replacing the first one, a second bird is chosen. what is the probability that both of the birds chosen are robins? round your answer to the nearest hundredth.

Explanation:

Step1: Calculate first - pick probability

The probability that the first bird is a robin is $\frac{14}{35}=\frac{2}{5}$.

Step2: Calculate second - pick probability

After one robin is taken, there are $14 - 1=13$ robins left and $35 - 1 = 34$ birds left. So the probability that the second bird is a robin given the first one was a robin is $\frac{13}{34}$.

Step3: Calculate joint probability

By the multiplication rule for dependent events, the probability that both are robins is $\frac{2}{5}\times\frac{13}{34}=\frac{26}{170}\approx0.15$.

Answer:

$0.15$