MHT CET 2024 16th May Evening Shift | Probability Question 1 | Mathematics

$\mathrm{P}[\mathrm{X}=x]=\left\{\begin{array}{cl}\frac{\mathrm{k}(x+1)}{5^x}, & \text { if } x=0,1,2 \ldots \ldots . \\ 0, & \text { otherwise }\end{array}\right.$

then $\mathrm{k}=$

$\frac{19}{25}$

$\frac{18}{25}$

$\frac{16}{25}$

$\frac{7}{25}$

MHT CET 2024 16th May Evening Shift

MCQ (Single Correct Answer)

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Numbers are selected at random, one at a time from two digit numbers $10,11,12 \ldots ., 99$ with replacement. An event $E$ occurs if and only if the product of the two digits of a selected number is 18 . If four numbers are selected, then probability that the event E occurs at least 3 times is

$\frac{87}{90^4}$

$\frac{348}{90^4}$

$87\left(\frac{4}{90}\right)^4$

$\left(\frac{4}{10}\right)^4$

MHT CET 2024 16th May Evening Shift

MCQ (Single Correct Answer)

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Two friends A and B apply for a job in the same company. The probabilities of A getting selected is $\frac{2}{5}$ and that of B is $\frac{4}{7}$. Then the probability, that one of them is selected, is

$\frac{8}{35}$

$\frac{18}{35}$

$\frac{26}{35}$

$\frac{34}{35}$

MHT CET 2024 16th May Morning Shift

MCQ (Single Correct Answer)

-0

If a random variable X has the following probability distribution values

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

Then $P(X \geq 6)$ has the value

$\frac{19}{100}$

$\frac{81}{100}$

$\frac{9}{100}$

$\frac{91}{100}$

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