Question

Вероятность того, что студентка получит по итогам сессии повышенную стипендию равна 10%, а того, что останется вообще без стипендии 40%. Какова вероятность, что за 5 сессий она ни разу не получит повышенную стипендию и два раза останется без стипендии?

Answer 1

Я буду писать не проценты, а дроби. 10% = 0,1; 40% = 0,4.
Вероятность, что она не получит повышенную, равна 1 - 0,1 = 0,9.
Что не получит ни разу за 5 сессий P0 = (0,9)^5 = 0,59049 ~ 0,59
Вероятность, что она 2 раза останется без стипендии и 3 раза получит
P2 = C(2, 5)*0,4^2*(1-0,4)^3 = 5*4/2*0,4^2*0,6^3 = 0,3456
Вероятность, что эти два события произойдут одновременно
P = P0*P2 = 0,59*0,3456 = 0,203904 ~ 0,204

Answer 2

Problem Analysis

We are given the following probabilities: - The probability of a student receiving an increased scholarship is 10%. - The probability of a student not receiving any scholarship is 40%.

We need to find the probability that a student will not receive an increased scholarship in 5 sessions and will not receive any scholarship in 2 sessions.

Solution

To find the probability, we can multiply the probabilities of each event happening.

Let's calculate the probability step by step:

1. Probability of not receiving an increased scholarship in one session: 90% (100% - 10%). 2. Probability of not receiving any scholarship in one session: 40%. 3. Probability of not receiving an increased scholarship in 5 sessions: (90%)^5. 4. Probability of not receiving any scholarship in 2 sessions: (40%)^2.

Now, let's calculate the final probability:

Probability of not receiving an increased scholarship in 5 sessions and not receiving any scholarship in 2 sessions: = Probability of not receiving an increased scholarship in 5 sessions * Probability of not receiving any scholarship in 2 sessions = (90%)^5 * (40%)^2

Calculating the final probability:

(90%)^5 * (40%)^2 = 0.59049 * 0.16 = 0.09447936

Therefore, the probability that the student will not receive an increased scholarship in 5 sessions and will not receive any scholarship in 2 sessions is approximately 0.0945 or 9.45%.