Probability Tes...

On tossing a fair coin for $$5$$ times, what is the probability that at least four of the five flips will be heads?

Calculate the probability that a number selected at random from the set {$$2,3,7,12,15,22,72,108$$} will be divisible by both $$2$$ and $$3$$.

For any two events $$A$$ and $$B$$, if $$\displaystyle P\left( A\cup B \right) =\dfrac {5}{6},\quad P\left( A\cap B \right) =\dfrac {1}{3},\quad P\left( B \right) =\dfrac {1}{2}$$, then $$\displaystyle P\left( A \right) $$ is:

On a certain day the chance of rain is $$80\%$$ in Delhi and $$30\%$$ in Hyderabad. Assume that the chance of rain in the two cities is independent. What is the probability that it will not rain in either city?

Four letters mailed today each have a probability of arriving in two days or sooner equal to $$\dfrac {2}{3}$$. Calculate the probability that exactly two of the four letters will arrive in two days or sooner.

Two dice are tossed once. The probability of getting an even number at the first die or a total of $$8$$ is

If $$A, B$$ and $$C$$ are mutually exclusive and exclusive events of a random experiment such that $$P(B)=\dfrac{3}{2}P(A)$$ and $$P(C)=\dfrac{1}{2}P(B)$$, then $$P(A \cup C)=$$

Let $$S$$ be a set containing $$n$$ elements and we select two subsets $$A$$ and $$B$$ of $$S$$ at random, then the probability that $$A\cup B=S$$ and $$A\cap B=\phi$$, is.

Let $$A$$ and $$B$$ be events in a sample space $$S$$ such that $$P(A)=0.5, P(B)=0.4$$ and $$P(A\cup B)=0.6$$. Observe the following lists:

In a sample survey of $$640$$ people, it was found that $$400$$ people have a secondary school certificate. If a person is selected at random, what is the probability that the person does not have such certificate?