alleryStart learning →The event E ∩ F is also written in which short form?
- E + F
- E / F
- EF
- E | F
Show answer and solution
Correct answer: C. EF
Writing two events side by side denotes that both occur, the same as their intersection.
CBSE Class 12 (Commerce) Probability — practice questions — page 3
Explore 80 free Probability questions in CBSE Class 12 (Commerce) Mathematics. Open each question or exercise to read its content, reference answers and available explanation.
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Showing questions 61–80 of 80.
The event E ∩ F is also written in which short form?Read the answer and worked solution →The event E ∩ F describes which situation?Read the answer and worked solution →Once F is known to have occurred, E is judged within which sample space?Read the answer and worked solution →A family has two children. Given at least one is a boy, P(both boys)?Read the answer and worked solution →Two dice are thrown. Given doubles, P(the sum is 8)?Read the answer and worked solution →Two dice are thrown. Given the first shows 5, P(sum is at least 10)?Read the answer and worked solution →One ace is drawn from a deck and kept aside. P(the next card is an ace)?Read the answer and worked solution →A fair coin is tossed twice. Given the first is tails, P(second is heads)?Read the answer and worked solution →P(A) = 0.6, P(B) = 0.5, P(A ∩ B) = 0.3. Find P(A|B).Read the answer and worked solution →A, B independent, P(A) = 0.2, P(B) = 0.5. Find P(A ∩ B').Read the answer and worked solution →Two archers hit with chances 0.7 and 0.8 independently. P(at least one hits)?Read the answer and worked solution →A fair coin is tossed 3 times. P(at least one head)?Read the answer and worked solution →1% are ill; test is + for 90% of ill, 5% of healthy. P(ill | +)?Read the answer and worked solution →Machine A makes 60% of items (2% faulty), B makes 40% (5% faulty). P(faulty)?Read the answer and worked solution →Bag I: 2 white, 3 red; Bag II: 4 white, 5 red. A bag is chosen at random. P(white)?Read the answer and worked solution →Bag I: 2 white, 3 red; Bag II: 4 white, 5 red. A white ball is drawn. P(Bag II)?Read the answer and worked solution →If P(E ∩ F) = 0.12 and P(F) = 0.4, find P(E|F).Read the answer and worked solution →In Bayes' theorem, the denominator sum of P(Ej)P(A|Ej) equalsRead the answer and worked solution →Two events are independent when one occurringRead the answer and worked solution →Two cards are drawn without replacement. P(a king, then a queen)?Read the answer and worked solution →
Worked practice questions
The event E ∩ F describes which situation?
- Both E and F occur
- Only E occurs here
- Only F occurs here
- Either one occurs
Show answer and solution
Correct answer: A. Both E and F occur
An outcome lies in the intersection only when it belongs to both events, so both happen at once.
Once F is known to have occurred, E is judged within which sample space?
- The whole space S
- The event E itself
- The complement of F
- The event F itself
Show answer and solution
Correct answer: D. The event F itself
Outcomes outside F are ruled out, so F becomes the new reduced sample space for E.
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