Q.If A and B are any two events, then which of the following is not true?

Showing the 12 most recent of 14 on this concept.

1. CBSE 2026Set ANNUAL1 mark
   Q.The sum of the probabilities of all the elementary events of an experiment is ______.

   ›Reveal solutionSolution

   The sum equals $1$.

   In any random experiment, the elementary events form the sample space $S$, and they are mutually exclusive and exhaustive (exactly one of them must occur). Since $P(S)=1$ and $S$ is the union of all elementary events, the sum of their individual pro …

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2. CBSE 2025Set sz1 markMCQ
   Q.For an event A if $P(A) = \dfrac{3}{5}$, then $P(A')$ is equal to :

   (a) \dfrac{7}{8}

   (b) \dfrac{5}{3}

   (c) \dfrac{2}{3}

   (d) \dfrac{2}{5}

   ›Reveal solutionSolution

   Complementary events satisfy $P(A) + P(A') = 1$, so with $P(A)=3/5$, $P(A')=2/5$.

   For any event $A$ and its complement $A'$ (the event that $A$ does not occur), the probabilities always satisfy:

   $P(A) + P(A') = 1.$

   Given $P(A) = \dfrac{3}{5}$: …

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3. CBSE 2025Set ANNUAL1 markMCQ
   Q.Which of the following cannot be the probability of occurrence of an event?

   (a) 0

   (b) $\dfrac{-3}{4}$

   (c) $\dfrac{3}{4}$

   (d) 1

   ›Reveal solutionSolution

   Probability values must always lie in the closed range $[0,1]$.

   $0$ and $1$ are the extreme allowed values, and $3/4$ lies between them — all valid. $-3/4$ is negativ …

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4. CBSE 2024Set ANNUAL1 markMCQ
   Q.If $\dfrac{3}{11}$ is probability of an event $A$, what is the probability of the event 'not $A$'?

   (a) $\dfrac{8}{11}$

   (b) $\dfrac{9}{11}$

   (c) $\dfrac{1}{11}$

   (d) None of these

   ›Reveal solutionSolution

   The probability of an event NOT happening is $1$ minus the probability that it does happen.

   Given $P(A) = \dfrac{3}{11}$, the complement rule states:

   $P(A') = 1 - P(A)$

   …

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5. CBSE 2024Set ANNUAL1 mark
   Q.If an event is impossible, then what will be its probability?

   ›Reveal solutionSolution

   By definition, an impossible event is the empty set $\varnothing$, and $P(\varnothing)=0$.

   An impossible event is one that can never occur under the given random experiment; it corresponds to the empty subset $\varnothing$ of the sample space.

   …

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6. CBSE 2024Set ANNUAL1 mark
   Q.Fill in the blank: $P(A) + P(\overline{A}) =$ ______.

   ›Reveal solutionSolution

   An event and its complement are exhaustive and mutually exclusive, so their probabilities sum to 1.

   Step 1. $A$ and $\overline{A}$ are mutually exclusive (they cannot both occur) and exhaustive (together they cover the whole sample space $S$).

   …

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7. CBSE 2023Set ANNUAL1 markMCQ
   Q.If $E$ is an impossible event, then $P(E) =$

   (a) 0

   (b) 4

   (c) 16

   (d) 2

   ›Reveal solutionSolution

   An impossible event has probability exactly 0, by definition.

   In probability theory, the sample space $S$ has $P(S)=1$. The impossible event is the empty set $\phi$ — an event that contains no outcome …

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8. CBSE 2023Set annual1 mark
   Q.If $P(A) = \dfrac{2}{5}$, find $P(\text{not } A)$.

   ›Reveal solutionSolution

   $P(\text{not }A) = 1 - P(A) = \dfrac{3}{5}$.

   For any event $A$, the event 'not $A$' (its complement) together with $A$ covers the whole sample space, so

   $P(A) + P(\text{not }A) = 1.$

   Given $P(A) = \dfrac{2}{5}$, …

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9. CBSE 2022Set ANNUAL1 markMCQ
   Q.If A and B are any two events, then which of the following is not true?

   (a) P(A ∩ B) ≤ P(A)

   (b) P(A ∩ B) ≤ P(A ∪ B)

   (c) P(A) ≤ P(A ∩ B)

   (d) P(B) ≤ P(A ∪ B)

   ›Reveal solutionSolution

   Since $A \cap B \subseteq A$, we always have $P(A \cap B) \le P(A)$ — the reverse inequality in (c) is false in general.

   For any two events $A, B$: $A \cap B \subseteq A$, $A \cap B \subseteq B$, and $A \cap B \subseteq A \cup B$.

   • (a) $P(A \cap B) \le P(A)$ — true, since $A \cap B \subseteq A$.
   • (b) $P(A \cap B) \le P(A \cup B)$ — true, since $A \cap B \subseteq A \cup B$. …

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10. CBSE 2022Set ANNUAL1 markMCQ
    Q.The probability of an event cannot be greater than.........

    (a) one

    (b) two

    (c) zero

    (d) three

    ›Reveal solutionSolution

    Probability cannot exceed $1$.

    For any event $E$, $0\le P(E)\le 1$; a certain event has probability $1$ and an impossible event $0$. So probability can never be greater than …

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11. CBSE 2021Set ANNUAL1 markMCQ
    Q.If A and B are any two events, then which of the following is not true?

    (a) P(A∩B) ≤ P(A∪B)

    (b) P(A∩B) ≤ P(A)

    (c) P(A) ≤ P(A∩B)

    (d) P(B) ≤ P(A∪B)

    ›Reveal solutionSolution

    Since $A \cap B \subseteq A$, we always have $P(A\cap B) \le P(A)$ — the reverse (option c) is the false one.

    For any two events, $A \cap B$ is a subset of both A and B, and also a subset of $A \cup B$. From basic set-subset monotonicity of probability ($X \subseteq Y \Rightarrow P(X) \le P(Y)$):

    • (a) $A\cap B \subseteq A\cup B \Rightarrow P(A\cap B)\le P(A\cup B)$ — true
    • (b) $A\cap B \subseteq A \Rightarrow P(A\cap B)\le P(A)$ — true
    • (d) $B \subseteq A\cup B \Rightarrow P(B)\le P(A\cup B)$ — true …

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12. CBSE 2021Set ANNUAL1 markMCQ
    Q.If 2/11 is the probability of an event then the probability of the event "not A" is:

    (a) 0

    (b) 2/11

    (c) 9/11

    (d) -2/11

    ›Reveal solutionSolution

    $P(\text{not }A) = 1 - P(A) = 9/11$.

    For any event A, $P(\text{not } A) = P(A') = 1 - P(A)$.

    …

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