A number of chosen at random from the set {1, 2, 3, ....., 2000}. Let p be the probability that the chosen number is a multiple of 3 or a multiple of 7. Then the value of 500p is __________.
Your Input ________
Answer
Correct Answer is 214
Explanation
Given, set = {1, 2, 3, ...., 2000}
Let E1 = Event that it is a multiple of 3 = {3, 6, 9, ...., 1998}
$$\therefore$$ n(E1) = 666
and E2 = Event that it is a multiple of 7 = {7, 14, ..., 1995}
Three numbers are chosen at random, one after another with replacement, from the set S = {1, 2, 3, ......, 100}. Let p1 be the probability that the maximum of chosen numbers is at least 81 and p2 be the probability that the minimum of chosen numbers is at most 40.
The value of $${{125} \over 4}{p_2}$$ is ___________.
Three numbers are chosen at random, one after another with replacement, from the set S = {1, 2, 3, ......, 100}. Let p1 be the probability that the maximum of chosen numbers is at least 81 and p2 be the probability that the minimum of chosen numbers is at most 40.
The value of $${{625} \over 4}{p_1}$$ is ___________.
Two fair dice, each with faces numbered 1, 2, 3, 4, 5 and 6, are rolled together and the sum of the numbers on the faces is observed. This process is repeated till the sum is either a prime number or a perfect square. Suppose the sum turns out to be a perfect square before it turns out to be a prime number. If p is the probability that this perfect square is an odd number, then the value of 14p is ..........
Your Input ________
Answer
Correct Answer is 8
Explanation
Let an event E of sum of outputs are perfect square (i.e., 4 or 9), so