Q.Fill in the blank: $P(A) + P(\overline{A}) =$ ______.

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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