If the error involved in making a certain measurement is a continuous random variable $X$ with probability density function $f(x) = k(4 - x^2)$ for $-2 \leq x \leq 2$ and $f(x) = 0$ otherwise,then $P[-1 < X < 1] = $
- A$\frac{13}{16}$
- B$\frac{1}{2}$
- C$\frac{1}{3}$
- D$\frac{11}{16}$
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In a game,$3$ coins are tossed. $A$ person is paid $₹150$ if he gets all heads or all tails,and he is supposed to pay $₹50$ if he gets one head or two heads. The amount he can expect to win or lose on an average per game in $₹$ is:
The probability that an individual suffers a bad reaction from an injection is $0.001$. The probability that out of $2000$ individuals exactly three will suffer a bad reaction is:
DifficultTS EAMCET 2011
View Solution$A$ random variable $X$ has the following probability distribution:
$X = x_i$ $1$ $2$ $3$ $4$ $5$ $6$ $7$ $8$ $9$ $P(X = x_i)$ $10k$ $9k$ $8k$ $8k$ $6k$ $5k$ $4k$ $3k$ $k$
where $k$ is a real number. If $A = \{ x_i : x_i \text{ is a prime number} \}$ and $B = \{ x_i : x_i > 5 \}$ are two events,then $P(A \cup B) = $
| $X = x_i$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ |
| $P(X = x_i)$ | $10k$ | $9k$ | $8k$ | $8k$ | $6k$ | $5k$ | $4k$ | $3k$ | $k$ |
where $k$ is a real number. If $A = \{ x_i : x_i \text{ is a prime number} \}$ and $B = \{ x_i : x_i > 5 \}$ are two events,then $P(A \cup B) = $
$A$ fair die is tossed repeatedly until a six is obtained. Let $X$ denote the number of tosses required and let $a=P(X=3)$,$b=P(X \geq 3)$ and $c=P(X \geq 6 \mid X>3)$. Then $\frac{b+c}{a}$ is equal to
DifficultJEE MAIN 2024
View SolutionIf the average number of accidents occurring at a particular junction on a highway in a week is $5$,then the probability that at most one accident occurs in a particular week is
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