Albino rats used to study the hormonal regulation of a metabolic pathway are injected with a drug that inhibits body synthesis of protein. Usually, 4 out of 20 rats die from the drug before the experiment is over. This time round, 10 animals are treated with the drug. What is the probability that 5 of these animals will die before the experiment is over?
0.8
0.0001
252
0.4032
0.0264
0.4032
This can be calculated using the binomial probability formula:
P(X = k) = (n choose k) * (p^k) * (1-p)^(n-k)
where:
n = total number of animals (10)
k = number of animals that will die (5)
p = probability of an animal dying (4 out of 20, or 0.2)
Plugging in the values:
P(X = 5) = (10 choose 5) * (0.2^5) * (0.8^5)
= 252 * (0.00032) * (0.32768)
= 0.4032
Therefore, the probability that exactly 5 out of the 10 animals treated with the drug will die before the experiment is over is 0.4032.