Question

В мешке 14 шаров из них 8 красных, а остальные жёлтого цвета, найдите вероятность того,что среди взятых наудачу трёх шаров есть хотя бы один красный( решить подробно) по формуле , пример типо -A-из них красных , что-то такого

Answer 1

Ответ:

P(A)≈0.95

Пошаговое объяснение:

14-8=6 жёлтых шаров

А - есть хотя бы один красный( может быть 1,2 или 3)

A¯ - противоположное событие- ни одного красного, т.е. все жёлтые.

P(A)=1-p(A¯)

Все жёлтые можно выбрать С₆³ способами.

А всего вариантов выбора С₁₄³

P(A¯)= С₆³/С₁₄³=(6!*11!*3!)/(3!*3!*14!)=(4*5*6)/(14*13*12)≈0.055

P(A)≈1-0.055≈0.95

Answer 2

Problem Statement

В мешке находится 14 шаров, из которых 8 красных, а остальные жёлтого цвета. Найдите вероятность того, что среди взятых наудачу трёх шаров есть хотя бы один красный.

Solution

To find the probability of drawing at least one red ball out of three randomly chosen balls, we can use the concept of complementary probability. The complementary probability is the probability of the event not occurring. In this case, it is the probability of not drawing any red balls.

Let's calculate the probability of not drawing any red balls: - There are 14 balls in total, out of which 8 are red and 6 are yellow. - The probability of not drawing a red ball on the first draw is 6/14. - After the first draw, there are 13 balls left in the bag, out of which 7 are yellow. - The probability of not drawing a red ball on the second draw is 7/13. - After the second draw, there are 12 balls left in the bag, out of which 6 are yellow. - The probability of not drawing a red ball on the third draw is 6/12.

To find the probability of not drawing any red balls in all three draws, we multiply the individual probabilities: (6/14) * (7/13) * (6/12) = 0.14285714285714285

The probability of not drawing any red balls is approximately 0.1429.

Now, to find the probability of drawing at least one red ball, we subtract the probability of not drawing any red balls from 1: 1 - 0.14285714285714285 = 0.8571428571428571

The probability of drawing at least one red ball out of three randomly chosen balls is approximately 0.8571.

Answer: The probability of drawing at least one red ball out of three randomly chosen balls is approximately 0.8571.