Question

Из ящика где хранятся 5 желтых и 7 красных карандашей продавец не глядя вынимает один за другим 3 карандаша .найди вероятность того что а)все карандаши окажутся желтыми Б)первые 2 карандаша -желтые , а третий -красный

Answer 1

б)первые 2 карандаша -желтые , а третий -красный

Answer 2

Problem Statement

В ящике хранятся 5 желтых и 7 красных карандашей. Продавец не глядя вынимает один за другим 3 карандаша. Найди вероятность того, что: а) все карандаши окажутся желтыми б) первые 2 карандаша - желтые, а третий - красный

Solution

To find the probability of these events, we need to calculate the total number of possible outcomes and the number of favorable outcomes.

Part a) All pencils are yellow

To find the probability that all pencils are yellow, we need to calculate the number of favorable outcomes where all three pencils drawn are yellow.

The total number of pencils in the box is 5 yellow + 7 red = 12 pencils.

The number of favorable outcomes is when all three pencils drawn are yellow, which is 5 yellow pencils.

Therefore, the probability that all pencils drawn are yellow is 5/12.

Part b) The first two pencils are yellow and the third pencil is red

To find the probability that the first two pencils drawn are yellow and the third pencil is red, we need to calculate the number of favorable outcomes where the first two pencils drawn are yellow and the third pencil drawn is red.

The total number of pencils in the box is 5 yellow + 7 red = 12 pencils.

The number of favorable outcomes is when the first two pencils drawn are yellow and the third pencil drawn is red. The probability of drawing a yellow pencil on the first draw is 5/12. After drawing a yellow pencil, there are 4 yellow pencils left out of 11 total pencils. Therefore, the probability of drawing a yellow pencil on the second draw is 4/11. Finally, the probability of drawing a red pencil on the third draw is 7/10.

Therefore, the probability that the first two pencils drawn are yellow and the third pencil drawn is red is (5/12) * (4/11) * (7/10) = 7/66.

Summary

a) The probability that all pencils drawn are yellow is 5/12. b) The probability that the first two pencils drawn are yellow and the third pencil drawn is red is 7/66.