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+1 vote
1.1k views
in Probability by (28.9k points)

In answering a question on a multiple choice test for class XII, a student either knows the answer or guesses. Let 3/5 be the probability that he knows the answer and 2/5 be the probability that he guesses. Assume that a student who guesses at the answer will be correct with probability 1/3. Let E1, E2, E be the events that the student knows the answer, guesses the answer and answers correctly respectively.

Based on the above information, answer the following

1. What is the value of P(E1)?

a. 2/5

b. 1/3

c. 1

d. 3/5

2. Value of P(E | E1) is

a. 1/3

b. 1

c. 2/3

d. 415

3. \(\sum^{k=2}_{k=1}\) P(E|Ek ) P(Ek)  Equals

a. 11/15

b. 4/15

c. 1/5

d. 1

4. Value of \(\sum_{k=1}^{k=2}\) P(Ek)

a. 1/3

b. 1/5

c. 1

d. 3/5

5. What is the probability that the student knows the answer given that he answered it correctly?

a. 2/11

b. 5/3

c. 9/11

d. 13/3

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2 Answers

+1 vote
by (29.8k points)

1. (d) 3/5

2. (b) 1

3. (a) 11/15

4. (c) 1

5. (c) 9/11

0 votes
by (49.1k points)

1. (d) \( \frac 35\)

\(P(E_1) = \frac 35\)

2. (b) 1

P(E|E1) = P(student answer correct | he knows answer) 

= Probability that student answers correctly,

If he knows the answer

= 1

3. (a) \(\frac{11}{15}\)

4. (c) 1

5. (c) \(\frac 9{11}\)

We need to find the Probability that the student knows the answer given that he answered it correctly

i.e. P(E1|E)

Now,

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