The probability of winning on the bonds of the loan for the entire period of its validity is 0.25.

The probability of winning on the bonds of the loan for the entire period of its validity is 0.25. What is the likelihood that someone who buys 8 bonds will win six of them?

The probability of winning on bonds is p = 0.25.
The probability of not winning q = 1 – p = 1 – 0.25 = 0.75.
According to Bernoulli’s formula, the probability of winning is 6 bonds out of 8.
P8 (6) = C (8.6) p ^ 6 q ^ 2;
The number of combinations of 8 elements of 6 is equal to:
C (8.6) = 8! / (6! (8 – 6)!) = 7 8 / (1 2) = 28.
P8 (6) = 28 0.25 ^ 6 0.75 ^ 2 = 28 0.00024 0.5625 = 0.0038.
Answer: 0.0038.