The probability of a certain event occurring in one trial = 0.4. Experiments are carried out before

The probability of a certain event occurring in one trial = 0.4. Experiments are carried out before the occurrence of the specified event. Find the probability that 4 tests will be carried out.

The probability that the event will occur in one test:
p = 0.4.

Let’s find the probability that the event will not occur:
q = 1 – p = 1 – 0.4 = 0.6.

For the fourth test to be carried out, it is necessary that in the first three the event does not occur even once. The likelihood of this is:
Q = q * q * q = 0.6 * 0.6 * 0.6 = 0.216.

Let’s multiply the result obtained by the probability of the event occurring in the fourth test:
P = Q * p = 0.216 * 0.4 = 0.0864.

Answer: The probability that the event will occur 4 trials is 0.0864.