Question

В экзаменационном билете один вопрос из трех разных тем. Первая тема содержит 20 вопросов, вторая — 30 и третья — 50. Студент знает ответы на 80% вопросов первой темы, на 85% вопросов второй и на все вопросы третей. Найти вероятность того, что: а) студент ответит на вопрос билета; б) вопрос, на который ответил студен, был из второй темы.

Answer 1

I=0,2 II=0,3 III=0,5 Ia=0.8 IIa=0.85 IIIa=1 a) P=I*Ia+II*IIa+III*IIIa=0,16+0,255+0.5=0.915 91.5% что он ответит. b)30/100=0.3 30% что вопрос из второй темы

Answer 2

Problem Analysis

In this problem, we are given an exam ticket with three different topics. The first topic has 20 questions, the second topic has 30 questions, and the third topic has 50 questions. The student knows the answers to 80% of the questions in the first topic, 85% of the questions in the second topic, and all the questions in the third topic. We need to find the probability that: a) The student answers a question from the ticket. b) The question the student answered is from the second topic.

Solution

Let's calculate the probabilities step by step.

a) Probability that the student answers a question from the ticket: To find this probability, we need to consider the total number of questions in all three topics and the percentage of questions the student knows the answers to in each topic.

The total number of questions in the ticket is: 20 (first topic) + 30 (second topic) + 50 (third topic) = 100 questions.

The student knows the answers to: 80% of 20 questions in the first topic = 0.8 * 20 = 16 questions. 85% of 30 questions in the second topic = 0.85 * 30 = 25.5 questions (rounded to the nearest whole number). All 50 questions in the third topic.

Therefore, the total number of questions the student knows the answers to is: 16 (first topic) + 25 (second topic) + 50 (third topic) = 91 questions.

The probability that the student answers a question from the ticket is: 91 (questions the student knows the answers to) / 100 (total questions in the ticket) = 0.91.

b) Probability that the question the student answered is from the second topic: To find this probability, we need to consider the number of questions in the second topic and the percentage of questions the student knows the answers to in the second topic.

The number of questions in the second topic is 30.

The student knows the answers to 85% of the questions in the second topic, which is 25.5 questions (rounded to the nearest whole number).

Therefore, the probability that the question the student answered is from the second topic is: 25.5 (questions the student knows the answers to in the second topic) / 30 (total questions in the second topic) = 0.85.

Summary

a) The probability that the student answers a question from the ticket is 0.91. b) The probability that the question the student answered is from the second topic is 0.85.

Please let me know if you need any further clarification.