The letters of the word PRABABILITY are written down at random in a row. Let `E_1` denotes the event that two Is are together and `E_2` denotes the event that `B ' s` are together, then `P(E_1)=P(E_2=3/(11)` (b) `P(E_1nnE_2)=2/(55)` `P(E_1uuE_2)=(18)/(55)` (d) `P((E_1)/(E_2))=1/5`

If E_(1) and E_(2) be two events such that P(E_(1))=0.3, P(E_(2))=0.2 and P(E_(1)nnE_(2))=0.1, then find: (i) P(barE_(1)nnE_(2)) (ii) P(E_(1)nnbarE_(2))

An urn contains four balls bearing numbers 1,2,3 and 123 respectively . A ball is drawn at random from the urn. Let E_(p) i = 1,2,3 donote the event that digit i appears on the ball drawn statement 1 : P(E_(1)capE_(2)) = P(E_(1) cap E_(3)) = P(E_(2) cap E_(3)) = (1)/(4) Statement 2 : P_(E_(1)) = P(E_(2)) = P(E_(3)) = (1)/(2)

If E' denote the complement of an event E , what is the value of P(E')+P( E )?

If E_(1) and E_(2) are two events such that P(E_(1))=1//4 , P(E_(2)//E_(1))=1//2 and P(E_(1)//E_(2))=1//4 , then

Let E and F be two independent events. The probability that exactly one of them occurs is 11/25 and the probability if none of them occurring is 2/25 . If P(T) denotes the probability of occurrence of the event T , then (a) P(E)=4/5,P(F)=3/5 (b) P(E)=1/5,P(F)=2/5 (c) P(E)=2/5,P(F)=1/5 (d) P(E)=3/5,P(F)=4/5

Let E and F be the events such that, P(E )=(1)/(3), P(F) = (1)/(4) and P(E cap F)=(1)/(5) , find P((barF)/(barE)) .

If E and F are two events such that P(E) =(1)/(4) ,P(F) = (1)/(2) and P(E nn F) = (1)/(8) , then find P( E' nn F')

For two events E_(1) and E_(2), P(E_(1))=1/2,P(E_(2))=1/3 and P(E_(1)nnE_(2))=1/10 . Find: (i) P(E_(1) "or" E_(2)) (ii) P(E_(1) "but not" E_(2)) (iii) P(E_(2)"but not" E_(1))

If E\ a n d\ E_2 are independent events, write the value of P(E_1uuE_2)nn( E_c1nn Ec_2)dot

A ship is fitted with three engines E_1,E_2 and E_3 . The engines function independently of each other with respective probabilities 1/2, 1/4, and 1/4 . For the ship to be operational at least two of its engines must function. Let X denote the event that the ship is operational and let X_1, X_2 and X_3 denote, respectively, the events that the engines E_1, E_2 and E_3 are function. Which of the following is/are true? (a) P(X_1^c "|"X)=3/(16) (b) P (exactly two engines of the ship are functioning "|"X ) =7/8 (c) P(X"|"X_2)=5/6 (d) P(X"|"X_1)=7/(16)