Algebra

Probability

Medium

Five numbers taken out from numbers 1-30 and arrange them in ascending order. The probability that the third number will be 20 is

$\frac{{}^{20}C_2 \times {}^{10}C_2}{{}^{30}C_5}$

$\frac{{}^{19}C_2 \times {}^{10}C_2}{{}^{30}C_5}$

$\frac{{}^{19}C_2 \times {}^{11}C_3}{{}^{30}C_5}$

$\frac{{}^{19}C_2 \times {}^{11}C_2}{{}^{30}C_5}$

✅ Correct Option: 2

For the third number (in ascending order) to be 20: choose 2 numbers smaller than 20 from $\{1,...,19\}$ in $^{19}C_2$ ways, and choose 2 numbers larger than 20 from $\{21,...,30\}$ in $^{10}C_2$ ways. Total ways to choose any 5 numbers from 30 is $^{30}C_5$ . Probability $= \frac{^{19}C_2 \times ^{10}C_2}{^{30}C_5}$ .

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A die is tossed four times. The probability of getting an odd number at least once, is

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If the random variable X has the following probability distribution:

X	0	1	2	Otherwise
P(X)	K	3K	5K	0

then K is equal to

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The probability that it will rain on any particular day is 50%. The probability that it rains only on the first 4 days of the week is:

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A and B are two independent events. The probability that both events A and B occur is $\frac{1}{6}$ and the probability that neither of them occur is $\frac{1}{3}$ . If P(A) = x, P(B) = y then the value of x+y is.

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The mean of the number of heads in a simultaneous toss of three coins is :

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If E and F are independent events associated with an experiment, then which one of the following statements is correct?

Five numbers taken out from numbers 1-30 and arrange them in ascending order. The probability that the third number will be 20 is

Solution

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