India plays two matches each against Australia and West Indies. The probabilities of India scoring $0, 1,$ and $2$ points in a match are $0.45, 0.05,$ and $0.50$ respectively. Assuming the results are independent,what is the probability that India scores at least $7$ points?
- A$0.875$
- B$0.0875$
- C$0.0625$
- D$0.025$
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In a city,$10$ accidents take place in a span of $50$ days. Assuming that the number of accidents follows the Poisson distribution,the probability that three or more accidents occur in a day is:
DifficultAP EAMCET 2016
View SolutionThe cumulative distribution function of a discrete random variable $X$ is given by the following table:
$X = x$ $-4$ $-2$ $0$ $2$ $4$ $6$ $8$ $10$ $F(X = x)$ $0.1$ $0.3$ $0.5$ $0.65$ $0.75$ $0.85$ $0.90$ $1$
Then,calculate $\frac{P(X \leqslant 0)}{P(X > 0)}$.
| $X = x$ | $-4$ | $-2$ | $0$ | $2$ | $4$ | $6$ | $8$ | $10$ |
|---|---|---|---|---|---|---|---|---|
| $F(X = x)$ | $0.1$ | $0.3$ | $0.5$ | $0.65$ | $0.75$ | $0.85$ | $0.90$ | $1$ |
Then,calculate $\frac{P(X \leqslant 0)}{P(X > 0)}$.
If $f(x) = \frac{x+2}{18}$ for $-2 < x < 4$ and $f(x) = 0$ otherwise,is the probability density function (p.d.f.) of a random variable $X$,then the value of $P(|X| < 2)$ is
The range of a random variable $X$ is $\{1, 2, 3, \ldots\}$ and $P(X=x) = \frac{c^x}{x!}$ for $x = 1, 2, 3, \ldots$. Then the value of $c$ is
The probability distribution of a random variable $X$ is given below:
$X$ $4k$ $\frac{30}{7}k$ $\frac{32}{7}k$ $\frac{34}{7}k$ $\frac{36}{7}k$ $\frac{38}{7}k$ $\frac{40}{7}k$ $6k$ $P(X)$ $\frac{2}{15}$ $\frac{1}{15}$ $\frac{2}{15}$ $\frac{1}{5}$ $\frac{1}{15}$ $\frac{2}{15}$ $\frac{1}{5}$ $\frac{1}{15}$
If $E(X) = \frac{263}{15}$, then $P(X < 20)$ is equal to:
| $X$ | $4k$ | $\frac{30}{7}k$ | $\frac{32}{7}k$ | $\frac{34}{7}k$ | $\frac{36}{7}k$ | $\frac{38}{7}k$ | $\frac{40}{7}k$ | $6k$ |
| $P(X)$ | $\frac{2}{15}$ | $\frac{1}{15}$ | $\frac{2}{15}$ | $\frac{1}{5}$ | $\frac{1}{15}$ | $\frac{2}{15}$ | $\frac{1}{5}$ | $\frac{1}{15}$ |
If $E(X) = \frac{263}{15}$, then $P(X < 20)$ is equal to:
DifficultJEE MAIN 2026
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