Question

Вероятность погашения кредита в срок равна 0,75. Найти вероятность того, что из 200 кредитов выданных банком будет погашено в срок: а) 175 кредитов, б) не менее 140 кредитов.помогите плиз

Answer 1

P(A) = C(175; 200) * 0,75¹⁷⁵*0,25²⁵ - вероятность, что 175 кредитов будут погашены вовремя

P(B) = $\sum_{k=140}^{200}C_{200}^{k}0,75^k*0,25^{200-k}$ - вероятность, что оплатят вовремя не менее 140 кредитов

Answer 2

Calculating the Probability of Loan Repayment

The probability of loan repayment is given as 0.75. We need to find the probability that out of 200 loans issued by the bank, a) 175 loans will be repaid on time, and b) at least 140 loans will be repaid on time.

Probability of 175 Loans Being Repaid on Time

The probability of 175 loans being repaid on time out of 200 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 trials (200 loans) - k = number of successful trials (175 loans) - p = probability of success (0.75)

Substituting the values: P(X = 175) = (200 choose 175) * (0.75^175) * ((1-0.75)^(200-175))

Let's calculate this probability.

Probability of At Least 140 Loans Being Repaid on Time

The probability of at least 140 loans being repaid on time can be calculated by summing the individual probabilities of 140, 141, ..., 200 loans being repaid on time. This can be quite complex to calculate manually, so we'll use a statistical calculator to find this probability.

Let's proceed with the calculations.