Statement-$I$: If a leap year is selected at random,the probability of it having $53$ Sundays is $2/7$.
Statement-$II$: $A$ leap year has $366$ days.
Statement-$II$: $A$ leap year has $366$ days.
- AStatement-$I$ is true. Statement-$II$ is true. Statement-$II$ is the correct explanation for Statement-$I$.
- BStatement-$I$ is true. Statement-$II$ is true. Statement-$II$ is not the correct explanation for Statement-$I$.
- CStatement-$I$ is true,Statement-$II$ is false.
- DStatement-$I$ is false,Statement-$II$ is true.
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The probability of at least one of the events $A$ and $B$ occurring is $0.6$. If $A$ and $B$ occur simultaneously with probability $0.2$, then $P(\overline{A}) + P(\overline{B})$ is
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View SolutionLet $A$ and $B$ be events in a sample space $S$ such that $P(A)=0.5, P(B)=0.4$ and $P(A \cup B)=0.6$. Observe the following lists. The correct match of List $I$ from List $II$ is:
List $I$ List $II$ $(i) \ P(A \cap B)$ $(1) \ 0.4$ $(ii) \ P(A \cap \bar{B})$ $(2) \ 0.2$ $(iii) \ P(\bar{A} \cap B)$ $(3) \ 0.3$ $(iv) \ P(\bar{A} \cap \bar{B})$ $(4) \ 0.1$
| List $I$ | List $II$ |
| $(i) \ P(A \cap B)$ | $(1) \ 0.4$ |
| $(ii) \ P(A \cap \bar{B})$ | $(2) \ 0.2$ |
| $(iii) \ P(\bar{A} \cap B)$ | $(3) \ 0.3$ |
| $(iv) \ P(\bar{A} \cap \bar{B})$ | $(4) \ 0.1$ |
If in a lottery there are $5$ prizes and $20$ blanks,then the probability of getting a prize is
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View SolutionIn the random experiment of tossing two unbiased dice, let $E$ be the event of getting the sum $8$ and $F$ be the event of getting even numbers on both the dice. Then:
$I. P(E) = \frac{7}{36}$
$II. P(F) = \frac{1}{3}$
Which of the following is a correct statement?
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$II. P(F) = \frac{1}{3}$
Which of the following is a correct statement?
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