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]
