MHT CET 2024 4th May Evening Shift | Probability Question 70 | Mathematics

A man and his wife appear for an interview for two posts. The probability of the husband's selection is $\frac{1}{7}$ and that of the wife's selection is $\frac{1}{5}$. If they appear for the interview independently, then the probability that only one of them is selected, is

$\frac{1}{7}$

$\frac{2}{7}$

$\frac{6}{7}$

$\frac{4}{7}$

MHT CET 2024 4th May Evening Shift

MCQ (Single Correct Answer)

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The expected value of the sum of the two numbers obtained on the uppermost faces, when two fair dice are rolled, is

MHT CET 2024 4th May Evening Shift

MCQ (Single Correct Answer)

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For an entry to a certain course, a candidate is given twenty problems to solve. If the probability that the candidate can solve any problem is $\frac{3}{7}$, then the probability that he is unable to solve at most two problem is

$\frac{256}{49}\left(\frac{4}{7}\right)^{18}$

$\frac{1966}{49}\left(\frac{4}{7}\right)^{18}$

$\frac{1710}{49}\left(\frac{4}{7}\right)^{18}$

$\frac{1726}{49}\left(\frac{4}{7}\right)^{18}$

MHT CET 2024 4th May Morning Shift

MCQ (Single Correct Answer)

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A random variable has the following probability distribution

$\mathrm{X:}$	0	1	2	3	4	5	6	7
$\mathrm{P}(x):$	0	$\mathrm{2p}$	$\mathrm{2p}$	$\mathrm{3p}$	$\mathrm{p^2}$	$\mathrm{2p^2}$	$\mathrm{7p^2}$	$\mathrm{2p}$

Then the value of p is

$\frac{1}{10}$

$\frac{1}{30}$

$\frac{1}{100}$

$\frac{3}{20}$

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