# Important Questions for Class 12 Chapter 13 - Probability

CBSE Board has laid down specific guidelines for the pattern of questions that a student of class 12th should be acquainted with. Adhering to these guidelines, we have come up with class 12th important questions which carries questions related to all topics in Mathematics.

Important questions based on NCERT syllabus for Class 12 Chapter 13 - Probability:

Question 1: Consider another example where a pack contains 5 blue, 3 red and 4 black pens. If a pen is drawn at random from the pack, replaced and the process repeated 2 more times, What is the probability of drawing 2 blue pens and 1 black pen?

Solution: Here, total number of pens = 12

Probability of drawing 1 blue pen = 5/12
Probability of drawing another blue pen = 5/12
Probability of drawing 1 black pen = 4/12
Probability of drawing 2 blue pens and 1 black pen = 5/12 * 5/12 * 4/12 = 25/288

Question 2: What is the probability of the occurrence of a number that is odd or less than 10 when a fair die is rolled.
Solution: Let the event of the occurrence of a number that is odd be ‘A’ and the event of the occurrence of a number that is less than 10 be ‘B’. We need to find P(A or B).

P(A) = 3/6 (odd numbers = 1,3 and 5)

P(B) = 9/6 (numbers less than 5 = 1,2,3 and 4)

P(A and B) = 5/6 (numbers that are both odd and less than 10 = 1,3, 5, 7 and 9)

Now, P(A or B) = P(A) + P(B) – P(A and B)

= 3/6 + 9/6 – 5/6

P(A or B) = 7/6.

Question 3: When two dice are rolled, find the probability of getting a greater number on the first die than the the second, given that the sum should equal 8.

Solution: Let the event of getting a greater number on the first die be G.

There are 3 ways to get a sum of 10 when two dice are rolled = {(5,5)(4,6)(6,4)}.

And there is only one ways where the number on the first die is greater than the one on the second given that the sum should equal 8, G = {(6,2)}.

Therefore, P(Sum equals 8) = 3/36 and P(G) = 1/36.

Now, P(G|sum equals 8) = P(G and sum equals 8)/P(sum equals 8)

= (3/36)/(1/36)

= 3