A die, whose faces are marked 1, 2, 3 in red and 4, 5, 6 in green, is tossed. Let A be the event “number obtained is even” and B be the event “number obtained is red”. Find if A and B are independent events.
Event A : Number obtained is even
B : Number obtained is red.
∴ A and B are not independent events.
B : Number obtained is red.
∴ A and B are not independent events.
If E and F are independent events, then show that
(i) E and F' are independent events.
(ii) E' and F are also independent events.
If E and F be two events such that P(E) = 1/3, P(F) = 1/4, find P(E U F) if E and F are independent events.
Prove that if E and F are independent events, then the events E and F' are also independent.
P speaks truth in 70% of the cases and Q in 80% of the cases. In what percent of cases are they likely to agree
in stating the same fact ?
A and B throw a pair of dice alternatively, till one of them gets a total of 10 and wins the game. Find their respective probabilities of winning, if A starts first.
A couple has 2 children. Find the probability that both are boys, if it is known that
(i) one of them is a boy
(ii) the older child is a boy.
Obtain the differential equation of the family of circles passing through the points (a, 0) and (– a, 0).
Prove that if E and F are independent events, then the events E and F' are also independent.
If E and F are two events such that P(E) = 1/4, P(F) = 1/2 and P(E ∩ F) = 1/8, find
(i) P(E or F)
(ii) P(not E and not F).
A box contains 50 bolts and 50 nuts. Half of the bolts and nuts are rusted. If two items are drawn with replacement, what is the probability that either both are rusted or both are bolts.