Probabilities are used to determine the chances of events.
The probability that at least 2 animals are infected is (c) 0.913
The proportion of the animal infected is given as:
[tex]p =60\%[/tex]
The probability is then calculated using the following binomial equation
[tex]P(x) = ^nC_xp^x(1-p)^{n-x}[/tex]
In this case,
[tex]n = 2[/tex]
To calculate the probability that at least 2 animals are infected, we start by calculating the probability that not up to 2 animals are infected.
So, we have:
[tex]P(x<2) =P(0) + P(1)[/tex]
This gives
[tex]P(x<2) = ^5C_0 \times (60\%)^0 \times (1-60\%)^{5-0}+ ^5C_1 \times (60\%)^1 \times (1-60\%)^{5-1}[/tex]
Simplify
[tex]P(x<2) = 1 \times (60\%)^0 \times (40\%)^{5}+ 5 \times (60\%) \times (40\%)^{4}[/tex]
[tex]P(x<2) = 0.08704[/tex]
Using the complement rule, we have:
[tex]P(x \ge 2) = 1 - P(x<2)[/tex]
So, we have:
[tex]P(x \ge 2) = 1 - 0.08704[/tex]
[tex]P(x \ge 2) = 0.91296[/tex]
Approximate
[tex]P(x \ge 2) = 0.913[/tex]
Hence, the probability is (c) 0.913
Read more about probabilities at:
https://brainly.com/question/251701
