An integer is chosen at random from the first 200 positive integers. The probability that the integer chosen is divisible by 6 or 8 is:
Let E = divisible by 6
F = divisible by 8
Number divisible by 6 are: 6, 12, 18, 24,….198 i.e.. There are 33 numbers in first 200 positive integers that are divisible by 6.
Number divisible by 8 are: 8, 16, 24, 32,….200 i.e.. There are 25 numbers in first 200 positive integers that are divisible by 8.
Number divisible by 6 and 8 both are: 24,….192. These are 8 numbers in first 200 positive integers that are divisible by both 6 and 8.
P(integer is divisible by 6 and 8) = P(E ∪ F) = P (E) + P(F)
A and B toss a coin alternatively till one of them gets a head and wins the game. If A begins the game, the probability B wins the game is
Suppose X ~ B(n, p) and P(X = 5). If p > 1/2, then
A person is known to speak the truth 4 time out of 5. He throws a dia and reports that it is a ace. The probability that it is actually a ace is
In a game called “odd man out man out”, m(m > 2) persons toss a coin to determine who will buy refreshments for the entire group. A person who gets an outcome different from that of the rest of the members of the group is called the odd man out. The probability that there is a loser in any game is
The chance of an event happening is the square of the chance of happening of second event but the odds against the first are the cube of the odds against the second. The chance of the events:
The odd against a certain event are 5: 2 and the odds in favour of another independent event are 6: 5 the probability that at least one of the events will happen is:
If A1, A2,….An are any n events, then
The probability that at least one of the event A and B occurs is 0.6 if A and B occur simultaneously with probability 0.2, then
Odds in favour of an event A is 2 to 1 and odds in favour of A∪ B are 3 to 1. Consistent with information the smallest and largest values for the probability of event B are given by:
If ten objects are distributed at random among ten persons, the probability that at least one of them will not get object is: