MHT CET 2025 19th April Morning Shift | Probability Question 32 | Mathematics

If a random variable $X$ follows the Binomial distribution $\mathrm{B}(33, \mathrm{p})$ such that $3 \mathrm{P}(\mathrm{X}=0)=\mathrm{P}(\mathrm{X}=1)$, then the variance of X is

$\frac{11}{144}$

$\frac{35}{48}$

$\frac{121}{48}$

$\frac{33}{144}$

MHT CET 2024 16th May Evening Shift

MCQ (Single Correct Answer)

-0

If a discrete random variable X is defined as follows

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

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)

-0

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)

-0

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

$\frac{8}{35}$

$\frac{18}{35}$

$\frac{26}{35}$

$\frac{34}{35}$

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