Probability - Online Test
Q1.
Let ( be a partition of a sample space and suppose that each of has nonzero probability. Let A be any event associated with S,then
Answer : Option A
Explaination / Solution:
Let {E1, E2, ...,En) be a partition of a sample space and suppose that each of E1, E2, ..., En has nonzero probability. Let A be any event associated with S,then P(A) = P(E1) P (A|E1) + P (E2) P (A|E2) + ... + P (En) P(A|En) .by addition law of probability.
Q2. If P(A) =, P(B) = and P(A ∪ B) = find P(A∩B)
Answer : Option A
Explaination / Solution:
Q3. Two events A and B will be independent, if
Answer : Option D
Explaination / Solution:
Two events A and B will be independent, then
Q4. If P(A) = and P(B) = , find P (A ∩ B) if A and B are independent events.
Answer : Option B
Explaination / Solution:
Since A and B are independent events .
Therefore ,
Therefore ,
Q5. The conditional probability of an event E, given the occurrence of the event F is given by
Answer : Option C
Explaination / Solution:
The conditional probability of an event E, given the occurrence of the event F is given by :
Q6. The conditional probability of an event E, given the occurrence of the event F lies between
Answer : Option C
Explaination / Solution:
As the probability of any event always lies between 0 and 1. Therefore , 0 ≤ P (E|F) ≤ 1.
Q7. The conditional probability of the event E', given that F has occurred is given by
Answer : Option C
Explaination / Solution:
we know that P(S/F) =1
P(E U E'|F)=1 since EUE' =S
P(E/F) +P(E'/F) =1 since E and E' are disjoint events
P(E'/F) = 1- P(E/F)
Q8. If E, F and G are events with P(G) ≠ 0 then P ((E ∪ F)|G) given by
Answer : Option C
Explaination / Solution:
P(EUF/G) ==
= +-
= P (E|G) + P (F|G) – P ((E ∩ F)|G)
Q9. If E and F are events then P (E ∩ F) =
Answer : Option C
Explaination / Solution:
If E and F are events then P (E ∩ F) = P (E) P (F|E), P (E) ≠ 0. By the defination of conditional probability of two events
Q10. Two coins are tossed once ,where E : tail appears on one coin , F : one coin shows head. Find P(E/F).
Answer : Option C
Explaination / Solution:
