1
MHT CET 2024 2nd May Evening Shift
MCQ (Single Correct Answer)
+2
-0

Three houses are available in a locality. Three persons apply for the houses. Each applies for one house without consulting others. The probability that all the three persons apply for the same house is

A
$\frac{1}{9}$
B
$\frac{2}{9}$
C
$\frac{7}{9}$
D
$\frac{8}{9}$
2
MHT CET 2024 2nd May Morning Shift
MCQ (Single Correct Answer)
+2
-0

A bag contains 4 Red and 6 Black balls. A ball is drawn at random from the bag, its colour is observed and this ball along with 3 additional balls of the same colour are returned to the bag. If now a ball is drawn at random from the bag, then the probability that this drawn ball is red is

A
$\frac{41}{65}$
B
$\frac{24}{65}$
C
$\frac{26}{65}$
D
$\frac{28}{65}$
3
MHT CET 2024 2nd May Morning Shift
MCQ (Single Correct Answer)
+2
-0

If a discrete random variable X takes values $0,1,2,3, \ldots \ldots$. with probability $\mathrm{P}(\mathrm{X}=x)=\mathrm{k}(x+1) 5^{-x}$, where k is a constant, then $\mathrm{P}(\mathrm{X}=0)$ is

A
$\frac{7}{25}$
B
$\frac{16}{25}$
C
$\frac{18}{25}$
D
$\frac{19}{25}$
4
MHT CET 2024 2nd May Morning Shift
MCQ (Single Correct Answer)
+2
-0

Ten bulbs are drawn successively, with replacement, from a lot containing $10 \%$ defective bulbs, then the probability that there is at least one defective bulb, is

A
$1-\left(\frac{1}{10}\right)^{10}$
B
$1-\left(\frac{3}{10}\right)^{10}$
C
$1-\left(\frac{9}{10}\right)^{10}$
D
$1-\left(\frac{7}{10}\right)^{10}$
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