Question

Вероятность осуществления некоторой химической реакции при проведении эксперимента определенного вида равна 0,8. Найти вероятность того, что данная реакция произойдет в трех из четырех проведенных экспериментов.

Answer 1

По формуле Бернулли, р=0,8, q=0,2, n=4.
P(3,4)=(C из 4 по 3)•0,8^3•0,2=4•0,512•0,2=0,4096

Answer 2

Probability of a Chemical Reaction Occurring

To find the probability of a chemical reaction occurring in three out of four experiments, given that the probability of the reaction occurring in a single experiment is 0.8, we can use the binomial probability formula.

The binomial probability formula is given by:

P(X=k) = C(n, k) * p^k * (1-p)^(n-k)

Where: - P(X=k) is the probability of getting exactly k successes in n trials, - C(n, k) is the number of combinations of n items taken k at a time, - p is the probability of success in a single trial, and - (1-p) is the probability of failure in a single trial.

In this case, we want to find the probability of the reaction occurring in three out of four experiments, so k = 3, n = 4, and p = 0.8.

Plugging these values into the formula, we get:

P(X=3) = C(4, 3) * 0.8^3 * (1-0.8)^(4-3)

Calculating this expression:

P(X=3) = 4 * 0.8^3 * 0.2^1

Simplifying further:

P(X=3) = 4 * 0.512 * 0.2

P(X=3) = 0.4096

Therefore, the probability of the chemical reaction occurring in three out of four experiments is approximately 0.4096 or 40.96%.