When a fisherman catches a fish, the probability that it is a young one is 0.23 . All young fishes are returned to the water. On the other hand, an adult fish is kept for eating later. Out of the five fishes caught by the fisherman, What is the probability that at most 3 are edible

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okpalawalter8 okpalawalter8 · Answer 1 · 2020-11-06T06:56:13+01:00

Answer:

The value is [tex]P(X = 3) = 0.0725[/tex]

Step-by-step explanation:

From the question we are told that

The probability catching a young fish is q = 0.23

The number of fish that was caught is n = 5

Generally the probability of catching a adult fish is mathematically represented as

[tex]p = 1 -q[/tex]

=> [tex]p = 1 - 0.23[/tex]

=> [tex]p = 0.77[/tex]

Generally for a fish to be edible it must be an adult fish.

Generally the distribution of the number of fish the fisher man caught follows a binomial distribution

i.e

[tex]X \~ \ \ \ B(n , p)[/tex]

and the probability distribution function for binomial distribution is

[tex]P(X = x) = ^{n}C_x * p^x * (1- p)^{n-x}[/tex]

Here C stands for combination hence we are going to be making use of the combination function in our calculators

So

[tex]P(X = 3) = \ ^5C_3 *(0.77)^{3} * (0.23)^{5- 3 }[/tex]

=> [tex]P(X = 3) = 3 * 0.45653 * 0.0529[/tex]

=> [tex]P(X = 3) = 0.0725[/tex]