zoe and her dad went ice - fishing this winter. they caught 7 total fish, including 5 trout. if on the last…

zoe and her dad went ice - fishing this winter. they caught 7 total fish, including 5 trout. if on the last day of the trip, zoe randomly selected 4 fish to donate to fishermen who hadnt caught any fish that day, what is the probability that all of them are trout? write your answer as a decimal rounded to four decimal places.

zoe and her dad went ice - fishing this winter. they caught 7 total fish, including 5 trout. if on the last day of the trip, zoe randomly selected 4 fish to donate to fishermen who hadnt caught any fish that day, what is the probability that all of them are trout? write your answer as a decimal rounded to four decimal places.

Answer

Explanation:

Step1: Calculate total combinations

We use the combination formula $C(n,r)=\frac{n!}{r!(n - r)!}$, where $n$ is the total number of items and $r$ is the number of items to be chosen. The total number of ways to choose 4 fish out of 7 is $C(7,4)=\frac{7!}{4!(7 - 4)!}=\frac{7!}{4!3!}=\frac{7\times6\times5}{3\times2\times1}=35$.

Step2: Calculate favorable combinations

The number of ways to choose 4 trout out of 5 is $C(5,4)=\frac{5!}{4!(5 - 4)!}=\frac{5!}{4!1!}=5$.

Step3: Calculate probability

The probability $P$ that all 4 chosen fish are trout is the number of favorable combinations divided by the total number of combinations. So $P=\frac{C(5,4)}{C(7,4)}=\frac{5}{35}=\frac{1}{7}\approx0.1429$.

Answer:

0.1429