A die is thrown twice and the sum of the numbers appearing is observed to be 6. Then the probability that the number 4 has appeared at least once, is

A coin is tossed 5 times, the probability of getting at least 3 heads is:

If A and B are independent events such that $P(A)=\dfrac{1}{2}$, $P(A\cup B)=\dfrac{3}{5}$ and $P(B)=p$, then value of p 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 that seed is of type $A_2$ given that seed germinate.

A beg contains 4 white and 6 red balls. Four balls are drawn at random, then match the probability of the numbers of white balls drawn. Where P(E) denotes the probability of an event E.

Then Match List-I with List-II

Choose the correct answer from the options given below:

The variance of number of heads in three tosses of a coin is :

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 $e^{-0.02} = 0.9802$)