Class 12 Maths Chapter 13 Probability: NCERT Solutions

Conditional Probability

• The main purpose of providing NCERT Solutions for Class 12 Maths Chapter 13 is to assist students in understanding conditional probability concepts.
• Chapter 13 of NCERT Class 12 Maths focuses on conditional probability, which is a measure of the probability of an event occurring given that another event has occurred.
• In this chapter, students learn in detail about conditional probability, including the concept of conditional probability, properties, and applications.

Conditional Probability Formulas and Examples

• The conditional probability formula is P(E|F) = P(E ∩ F) / P(F), where E and F are events.
• To find the conditional probability of obtaining a sum greater than 9, given that the black die resulted in a 5, use the formula and plug in the given values.
• If P(E) = 0.6, P(F) = 0.3, and P(E ∩ F) = 0.2, then P(E|F) = P(E ∩ F) / P(F) = 0.2 / 0.3 = 2/3.
• In a family with two children, the conditional probability that both are girls given that the youngest is a girl can be found using the formula.
• Compute P(A|B), if P(B) = 0.5 and P(A ∩ B) = 0.32, using the formula.
• If P(A) = 0.8, P(B) = 0.5, and P(B|A) = 0.4, find P(A ∪ B) using the formula.
• Evaluate P(A ∪ B), if 2P(A) = P(B) = 5/13 and P(A|B) = 2/5.
• If P(A) = 6/11, P(B) = 5/11, and P(A ∪ B) = 7/11, find P(B|A) using the formula.

More Examples and Applications

• A fair die is rolled, and the conditional probability of event E occurring, given that event F has occurred, can be found using the formula.
• Find P(E|F), where E = {1,3,5}, F = {2,3}.
• The conditional probability of obtaining the sum 8, given that the red die resulted in a number less than 4, can be found using the formula.
• In a family with two children, the conditional probability that at least one is a girl given that at least one is a boy can be found using the formula.