The monthly expectation of a two-wheeler accident at a particular railway crossing is 0.02. What is the probability that in a specific month, no accident occurred? (given $e^{-0.02} = 0.9802$)

Three urns contain 6 red, 4 black; 4 red, 6 black and 5 red, 5 black marbles respectively. One of the urns is selected at random and a marble is drawn from it. If the marble drawn is red, then the probability that it is drawn from the first urn is

If A and B are two independent events with $P(A) = \frac{1}{5}$ and $P(B) = \frac{1}{3}$, then $P(A'/B)$ is:

A shopkeeper sells three types of flower seeds $A_1, A_2, A_3$. They are sold as a mixture where the proportions are 4 : 4 : 2 respectively. The germination rates of the three types of seeds are 45%, 60% and 35% respectively. Calculate the probability in the following cases.

The probability of a randomly chosen seed to germinate is :

An alphabet has been selected from English alphabets. What is the probability that it is a vowel given that it precedes 'M' ?

In a game, a man wins Rs. 5 for getting a number greater than 4 and loses Rs. 1 otherwise, when a fair dice is thrown. The man decided to throw a die thrice but to quit as and when he gets a number greater than 4. The expected value of the amount(in Rs.) he wins or loses is:

A man is known to speak the truth 3 out of 4 times. He throw a die and reports that it is five then the probability that it is actually five is