alleryFor any two events A and B, $P(A\cup B)$ equals:
- $P(A)P(B)$
- $P(A)-P(B)$
- $P(A)+P(B)-P(A\cap B)$
- $P(A)+P(B)$
Show answer and solution
Correct answer: C. $P(A)+P(B)-P(A\cap B)$
Addition theorem: P(A∪B) = P(A) + P(B) − P(A∩B).
AP Intermediate 2nd Year Probability — practice questions — page 2
Explore 51 free Probability questions in AP Intermediate 2nd Year Mathematics. Open each question or exercise to read its content, reference answers and available explanation.
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Showing questions 31–51 of 51.
For any two events A and B, $P(A\cup B)$ equals:Read the answer and worked solution →In the classical definition, the probability of an event E is:Read the answer and worked solution →Three fair coins are tossed simultaneously. The probability of getting EXACTLY two heads isRead the answer and worked solution →A card is drawn from a standard deck of 52. The probability that it is a KING or a QUEEN isRead the answer and worked solution →If $P(A) = 0.4$ and $P(B) = 0.5$ and $P(A \cap B) = 0.2$, then $P(A \cup B)$ isRead the answer and worked solution →What is the probability that a randomly drawn card from a 52-card deck is a FACE CARD (King, Queen, or Jack)?Read the answer and worked solution →Two events $A$ and $B$ are MUTUALLY EXCLUSIVE ifRead the answer and worked solution →Two fair coins are tossed. The probability of getting AT LEAST ONE head isRead the answer and worked solution →If the probability that a student passes a CAT mock test is $0.6$, what is the probability that the student FAILS?Read the answer and worked solution →SAT · Mathematics · Probability — Spot the ErrorRead the answer and worked solution →GMAT · Quantitativeaptitude · Probability — Spot ErrorRead the answer and worked solution →Match the probability term to its formulaRead the answer and worked solution →Probability claims — true or false?Read the answer and worked solution →A coin is tossed once. The probability of getting heads isRead the answer and worked solution →A die is rolled. The probability of getting an even number isRead the answer and worked solution →Probability of a sure event isRead the answer and worked solution →Two coins are tossed. The probability of getting two heads isRead the answer and worked solution →A card is drawn from a standard deck of 52 cards. The probability of drawing an ace isRead the answer and worked solution →Three coins are tossed. The probability of getting at least one head isRead the answer and worked solution →From a deck of 52 cards, one is drawn. The probability that it is a red queen isRead the answer and worked solution →A bag has 3 red and 5 blue balls. One ball drawn at random. Probability it is red isRead the answer and worked solution →
Worked practice questions
In the classical definition, the probability of an event E is:
- $\dfrac{\text{favourable outcomes}}{\text{total outcomes}}$
- favourable outcomes only
- total outcomes only
- $\text{favourable}\times\text{total}$
Show answer and solution
Correct answer: A. $\dfrac{\text{favourable outcomes}}{\text{total outcomes}}$
Classical probability = (number of favourable outcomes)/(total number of equally-likely outcomes).
Three fair coins are tossed simultaneously. The probability of getting EXACTLY two heads is
- $1/8$
- $2/8 = 1/4$
- $3/8$
- $4/8 = 1/2$
Show answer and solution
Correct answer: C. $3/8$
1. Sample space: $|S| = 2^3 = 8$ outcomes — HHH, HHT, HTH, HTT, THH, THT, TTH, TTT.
2. Event 'exactly 2 heads': enumerate — HHT, HTH, THH. So $|E| = 3$.
3. $P(\text{exactly 2 H}) = 3/8$.
4. Alternative via binomial probability: $P(\text{exactly}\,k\,\text{heads}) = \binom{n}{k}\,(1/2)^k\,(1/2)^{n-k} = \binom{n}{k}/2^n$. For $n = 3, k = 2$: $\binom{3}{2}/8 = 3/8$ ✓.
5. Option A is the probability of EXACTLY 0 or 3 heads. Option B is wrong count. Option D would require half of all outcomes.
_Source: syllabus Mathematics, Ch 14, Example 3 (Three-coin events), p. 4–5._
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