The Central Board of Secondary Education, CBSE, has scheduled the CBSE Class 12th Mathematics Examination 2020 on March 17, 2020. The students appearing in the CBSE Class 12th Mathematics Board Examination 2020 can go through the below-mentioned questions for Chapter 13- Probability. These Questions are based on the latest CBSE pattern.

**Question 1- **For a loaded die, the probabilities of outcomes are given as under *P *(l) = *P *(2) = 0.2, *P *(3) =*P *(5) *= P*(*6*)*= *0.1 and *P *(4) = 0.3. The die is thrown two times. Let *A *and 6 be the events, ‘the same number each time’ and ‘a total score is 10 or more’, respectively. Determine whether or not *A *and *B *are independent.

**Answer:** *P *(*A*) =** **0.20 ; *P*(*B*)* *= 0.10

A and B are independent events.

**Question 2- **

**Answer:** 1.1

**Question 3- **A bag contains 5 red marbles and 3 black marbles. Three marbles are drawn one by one without replacement. What is the probability that at least one of the three marbles drawn be black if the first marble is red?

**Answer: **P(E) = 25/56

**Question 4- **

**Answer: **(i) *P *( *A */ *B*) = 3/4

(ii) *P *( *B */ *A*) = 1/2

(iii) *P *( *A’ */ *B*) = 1/4

(iv) *P *( *A’ */ *B’*) = 5/8

**Question 5- **

**Answer: **(i) k = 1/3

(ii) Mean of the distribution (μ) = 23/18

**Question 6-** If X is the number of tails in three tosses of a coin, then determine the standard deviation of X.

**Answer: **standard deviation of X = **√**3 / 2.

**Question 7-** Three dice are thrown at the same time. Find the probability of getting three two’s, if it is known that the sum of the numbers on the dice was six.

**Answer: ***P (E _{2} / E_{1})*

**=**1/10

**Question 8- ** Four cards are successively drawn without replacement from a deck of 52 playing cards. What is the probability that all four cards are king?

**Answer: **1 / 270725

**Question 9-** A bag contains (*2n +*1) coins. It is known that *n *of these coins have a head on both sides whereas the rest of the coins are fair. A coin is picked up at random from the bag and is tossed. If the probability that the toss results in a head is 31/42, then determine the value of *n.*

**Answer:** n = 10

**Question 10-** There are 5 cards numbered 1 to 5, one number on one card. Two cards are drawn at random without replacement. Let *X *denotes the sum of the numbers on two cards drawn. Find the mean and variance of *X.*

**Answer:** Mean, E (*X*) = 6 and var (*X*) = 3

These questions are strictly based on the latest CBSE pattern prescribed by the CBSE Board. The students appearing for the CBSE Class 12th Mathematics Examination 2020 will find these questions helpful while preparing for the upcoming Examination.