MHT CET 2023 14th May Evening Shift | Probability Question 3 | Mathematics

A lot of 100 bulbs contains 10 defective bulbs. Five bulbs are selected at random from the lot and are sent to retail store. Then the probability that the store will receive at most one defective bulb is

$$\frac{7}{5}\left(\frac{9}{10}\right)^4$$

$$\frac{7}{5}\left(\frac{9}{10}\right)^5$$

$$\frac{6}{5}\left(\frac{9}{10}\right)^4$$

$$\frac{6}{5}\left(\frac{9}{10}\right)^5$$

MHT CET 2023 14th May Morning Shift

MCQ (Single Correct Answer)

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Two cards are drawn successively with replacement from well shuffled pack of 52 cards, then the probability distribution of number of queens is

$$\mathrm{X}=x$$	0	1	2
$$\mathrm{P[X=}x]$$	$$\frac{144}{169}$$	$$\frac{24}{169}$$	$$\frac{1}{169}$$

$$\mathrm{X}=x$$	0	1	2
$$\mathrm{P[X=}x]$$	$$\frac{1}{169}$$	$$\frac{24}{169}$$	$$\frac{144}{169}$$

$$\mathrm{X}=x$$	0	1	2
$$\mathrm{P[X=}x]$$	$$\frac{24}{169}$$	$$\frac{1}{169}$$	$$\frac{144}{169}$$

$$\mathrm{X}=x$$	0	1	2
$$\mathrm{P[X=}x]$$	$$\frac{1}{169}$$	$$\frac{25}{169}$$	$$\frac{143}{169}$$

MHT CET 2023 14th May Morning Shift

MCQ (Single Correct Answer)

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For an initial screening of an entrance exam, a candidate is given fifty problems to solve. If the probability that the candidate can solve any problem is $$\frac{4}{5}$$, then the probability, that he is unable to solve less than two problems, is

$$\frac{201}{5}\left(\frac{1}{5}\right)^{49}$$

$$\frac{316}{25}\left(\frac{4}{5}\right)^{48}$$

$$\frac{54}{5}\left(\frac{4}{5}\right)^{49}$$

$$\frac{164}{25}\left(\frac{1}{5}\right)^{48}$$

MHT CET 2023 14th May Morning Shift

MCQ (Single Correct Answer)

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$$\text { If } f(x)= \begin{cases}3\left(1-2 x^2\right) & ; 0< x < 1 \\ 0 & ; \text { otherwise }\end{cases}$$ is a probability density function of $$\mathrm{X}$$, then $$\mathrm{P}\left(\frac{1}{4} < x < \frac{1}{3}\right)$$ is

$$\frac{75}{243}$$

$$\frac{23}{96}$$

$$\frac{179}{864}$$

$$\frac{52}{243}$$

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