How many are two-digital positive integers multiple of 3?

If A and B are two events associated with a random experiment such that P(A)=0.3.P(B)=0.2 and \(P(A\cap B)=0.1\) ,then find the value of \(P(A\cap B)\)

Find the probability that in a random arrangement of the letters of the word 'SOCIAL' vowels come together.

In a lottery, a person choose 4 different natural numbers at random from 1 to 30 and there four numbers match with the six numbers already fixed by the lottery committee, he wins the prize.What is the probability of winning the prize in the game?

Abox contains 5 slips marked 1, 2, 3,4 and 5.Write the sample space of the experiment when
(i) one slip is drawn
(ii) one slip is drawn and not replaced then a second slip is drawn.

A die is thrown twice. Each time the number appearing on it is recorded. Describe the events.
A: both numbers are odd
B: both numbers are even
C: sum of the numbers is less than 6
Also find A u B, A n B, A u C and A n C. Which pairs of events are mutually exclusive?

A coin is tossed twice, what is the probability that atleast one tail occurs?

In a single throw of two die, find the probability of getting the sum neither 9 nor 11.

In a single throw of two die, what is the probability that the sum of the numbers on the two faces is either 9 or 11.

One natural number is selected from the first 20 natural numbers. What is the probability that it is either a prime number or an odd number?

Suppose that each child born is equally likely to be a boy or a girl. Consider a family with exactly three children.
List the eight elements in the sample space whose outcomes are all possible genders of the three children.

A and B are two events that P(A) = 0.54, P(B) = 0.69 and \(P(A\cap B)\) = 0.35. Find \(P(B\cap A')\)

Events E and F are such that P(not E or not F) = 0.25. State whether E and F are mutually exclusive.

A coin is tossed. If it shows a tail, we draw a ball from a box which contains 2 red and 3 black balls. If it shows head, we throw a die. Find the sample space for this experiment.

Two die are thrown. The events A, B, C are as follows:
getting an odd number on the first die.

A bag contains 6 discs of which 4 red,3 are blue and 2 are yellow.The discs are similar in shape and size.A disc is drawn at random from the bag.Calculate the probability that it will be
blue

A bag contains 6 discs of which 4 red,3 are blue and 2 are yellow.The discs are similar in shape and size.A disc is drawn at random from the bag.Calculate the probability that it will be
either red or blue

Fill in the blanks in following table:
\(P(A)\quad P(B)\quad P(A\cap B)\quad P(A\cup B)\)
\( i)\quad \frac { 1 }{ 3 } \quad \frac { 1 }{ 5 } \quad \frac { 1 }{ 15 } \quad ...\)
\(ii)\quad 0.35\quad ...\quad ...\quad 0.25\quad 0.6\)
\(iii)\quad 0.5\quad 0.35\quad ...\quad 0.7\)

From the employees of a company, 5persons are selected to represents them in the managing committee of the company's particulars of five persons are as follows

A person is selected at random from this group to act as a spokesperson. What is the probability that the spokesperson will be either male or over 35 years?

The number lock of a suitcase has 4 wheels, each labelled with ten digits i.e. from 0 to 9. The lock opens with a sequence of four digits with no repeats. What is the probability of a person getting the right sequence to open the suitcase?

A die is thrown, find the probability of following events:
(i) A prime number will appear.
(ii) A number greater than or equal to 3 will appear.
(iii) A number less than or equal to one will appear.
(iv) A number more than 6 will appear.
(v) A number less than 6 will appear.