##
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 1/5. Let E
_{
1
}
, E
_{
2
}
, 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:

##
**
Question 1
**

##
What is the value of P(E
_{
1
}
)?

## (a) 2/5

## (b) 1/3

## (c) 1

## (d) 3/5

##
**
Question 2
**

##
Value of P(E | E
_{
1
}
) is

## (a) 1/3

## (b) 1

## (c) 2/3

## (d) 415

##
**
Question 3
**

##
∑_(k=1) (k = 2) P(E│E
_{
k
}
) P(E
_{
k
}
) Equal

## (a) 11/15

## (b) 4/15

## (c) 1/5

## (d) 1

##
**
Question 4
**

##
Value of ∑_(k = 1) (k = 2) P(E
_{
k
}
)

## (a) 1/3

## (b) 1/5

## (c) 1

## (d) 3/5

##
**
Question 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