kwizNET Subscribers, please login to turn off the Ads!
Email us to get an instant 20% discount on highly effective K-12 Math & English kwizNET Programs!

Online Quiz (Worksheet A B C D)

Questions Per Quiz = 2 4 6 8 10

High School Mathematics - 2
Conditional Probability

Conditional Probability

Suppose a card is removed from a pack of cards and kept aside.
Let B be the event that the card is a spade.
After this one card is drawn at random from the remaining 51 cards.
Let A be the event that the second card is a spade. Under the assumption that B has happened n(A) = 12
P(A/B) = 12/51
It is read as probability of A when B has taken place or probability of A under B.
P(A/B) = n(A B ) / n(B)

Multiplication Theorem of Probability

    If A and B are any 2 events such that
  • P(A) ≠ 0
    then P(A B ) = P(A) . P(B/A)
  • P(B) ≠ 0
    then P(A B) = P(B).P(A/B)
  • P(B/A) = P(B)( i.e. Independent events)
    then P(A/B) = P(A)
Solved Examples
  1. A card is drawn from a pack of cards . Given that it is a heart, what is the probability that it is not a face card?

    A = The card is a heart.
    B = It is not a face card.
    As there are 3 face cards of heart, n(A B ) = 13-3 = 10.
    n(A) = 13
    So the required probability is
    P(B/A) = n(A B )/n(A) = 10/13

  2. The probability that a student A can solve a problem is 2/3 and B can solve it 5/8 and C can solve it is 1/4. If all of them try it independently, what is the probability that the problem is solved.

    Given P(A) = 2/3, P(B) = 5/8, P(C) = 1/4
    So P() = 1/3, P(B') = 3/8, P(C') = 3/4.
    Consider the event that the problem is not solved. i.e. B' C';
    So the required probability is
    P(problem solved) = 1 - P(problem not solved)
    = 1 - P( B' C';)
    = 1 - P().P(B').P(C')
    = 1 - (1/3.3/8.3/4)
    = 29/32

  3. One bag contains 4 apples and 3 mangoes and another contains 3 apples and 6 mangoes. One fruit is transferred at random from the first bag to the second and then a fruit is selected from the second bag. Find the probability that the fruit selected is an apple.

    Let A be the event that an apple is transferred from the first bag and let B be the event that an apple is selected from the second bag.
    So B may happen with A or
    So B = (A B ) U (A' B)
    A B and B are mutually exclusive.
    So P(B) = P(A B) + P( B).
    P( A B) = P(A) . P(B/A)
    = 4/7.4/10= 16/70
    P( B) = P() . P( B/)
    = 3/7.3/10
    So P(B) = P( A B) + P( B)
    = 16/70 + 9/70 = 25/70 = 5/14
    So P(B) = 5/14

Have your essay responses graded by your teacher and enter your score here!

Your score for this chapter (0-100%) =

Subscription to kwizNET Learning System offers the following benefits:

  • Unrestricted access to grade appropriate lessons, quizzes, & printable worksheets
  • Instant scoring of online quizzes
  • Progress tracking and award certificates to keep your student motivated
  • Unlimited practice with auto-generated 'WIZ MATH' quizzes
  • Child-friendly website with no advertisements
  • Choice of Math, English, Science, & Social Studies Curriculums
  • Excellent value for K-12 and ACT, SAT, & TOEFL Test Preparation
  • Get discount offers by sending an email to

Quiz Timer