1
MHT CET 2024 10th May Morning Shift
MCQ (Single Correct Answer)
+2
-0

In a Binomial distribution consisting of 5 independent trials, probabilities of exactly 1 and 2 successes are 0.4096 and 0.2048 respectively, then the probability, of getting exactly 4 successes, is

A
$\frac{80}{243}$
B
$\frac{40}{243}$
C
$\frac{32}{625}$
D
$\frac{4}{625}$
2
MHT CET 2024 10th May Morning Shift
MCQ (Single Correct Answer)
+2
-0

A random variable X has the following probability distribution

$\mathrm{X}$ 1 2 3 4 5 6 7 8
$\mathrm{P(X=}x)$ 0.15 0.23 0.12 0.10 0.20 0.08 0.07 0.05

For the events $\mathrm{E}=\{\mathrm{X}$ is prime number $\}$

$$\mathrm{F}=\{\mathrm{X}<4\}$$

Then $P(E \cup F)=$

A
0.87
B
0.77
C
0.35
D
0.50
3
MHT CET 2024 10th May Morning Shift
MCQ (Single Correct Answer)
+2
-0
 

There are three events $\mathrm{A}, \mathrm{B}, \mathrm{C}$, one of which must and only one can happen. The odds are 8:3 against $\mathrm{A}, 5: 2$ against B and the odds against C is $43: 17 \mathrm{k}$, then value of k is

A
$\frac{1}{2}$
B
2
C
$\frac{1}{3}$
D
$\frac{1}{4}$
4
MHT CET 2024 9th May Evening Shift
MCQ (Single Correct Answer)
+2
-0

Four persons can hit a target correctly with probabilities $\frac{1}{2}, \frac{1}{3}, \frac{1}{4}$ and $\frac{1}{5}$ respectively. If all hit at the target independently, then the probability that the target would be hit, is

A
$\frac{1}{5}$
B
$\frac{3}{5}$
C
$\frac{2}{5}$
D
$\frac{4}{5}$
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