Lecture on Conditional Probability

Details

• Presenter: Dr. Gajend Pravita
• Topic: Conditional Probability
• Target Audience: B.Sc., Engineering students, and exam-preparing students

Conditional Probability

• Definition:
  • Probability of event B given that event A has already occurred.
  • It is denoted as: P(A|B)
• Formula:
  • P(A|B) = P(A ∩ B) / P(B)
  • If A and B are independent, then P(A ∩ B) = P(A) * P(B)

Multiplication Theorem

• If events A and B are independent:
  • P(A|B) = P(A)
• If events are dependent:
  • P(A|B) = P(A ∩ B) / P(B)

Examples

Example 1: Dice

• When a die is rolled:
  • A = getting an odd number
  • B = getting a prime number
• Question: Find the probability of getting a prime number if an odd number appears.
  • Solution: P(A ∩ B) / P(B)

Example 2: Bat and Good Tube

• Extracting applications from two tubes
  • A and B: both are good
• Question: Find the probability that the other is good given one is extracted.

Example on Student Failure

• 20% students failed in English
• 15% students failed in Math
• 10% students failed in both
• Question: Find the probability that a student who failed in Math also failed in English.

Example of Drawing Balls

• 10 white and 5 black balls
• Drawing balls without replacement
• Find the probability that both are white.

Example Related to Cards

• Pack of 52 cards
• Question: Find the probability of drawing a red queen first and then a black king.

Conclusion

• Discussed Conditional Probability, Multiplication Theorem, and student failures.
• For more information, students can download the Maths Care App and join the Telegram group.

Contact Information

• For CSIR, NET, GATE, CUTPG exam preparation, contact for information.