Probability Tes...

A random variable $$X$$ has the probability distribution:

What is the probability that a number selected from the numbers 1, 2, 3, 4, 5......,16 is a prime number ?

Let A be a set containing n elements. A subset P of the set A is chosen at random.The set A is reconstructed by replacing the elements of $$P$$ and another subset $$Q$$ of A is chosen at random. The probability that $$ P \cap Q$$ contains exactly $$ m(m < n) $$ elements is

If $$E$$ and $$F$$ be events in a sample space such that $$\displaystyle P(E\cup F)=0.8,P(E\cap F)=0.3$$ and $$P(E) = 0.5$$, then $$P (F)$$ is

In figure points A, B, C and D are the centre of four circles that each have a radius of length one unit. If a point is selected at random from the interior of square ABCD. What is the probability that the point will be chosen from the shaded region?

In a survey of $$45$$ houses, it was found that $$25$$ have cars and $$30$$ have two-wheelers. How many have both?

Which of the following statements is true?

If $$P\left ( A/B \right )=0.2$$ and $$P\left ( B \right )=0.5$$ and $$P\left ( A \right )=0.3.$$ Find $$P\left ( A\cap \bar{B} \right ).$$

In a class of $$50$$ boys, $$35$$ like horror movies, $$30$$ like war movies and $$5$$ like neither. Find the number of those that like both.

Let A, B, C be three events such that P (A) = 0.3 P(B) = 0.4, P(C) = 0.8, P(A $$\cap$$ B) = 0.08, P(A $$\cap$$ C) = 0.28, P(A $$\cap$$ B $$\cap$$ C) = 0.09. If P(A $$\cup$$ B $$\cup$$ C) $$\geq $$ 0.75, then