Applied Mathematics

Probability Distribution

Hard

applied

In binomial distribution with $n = 10$ and $P = \frac{1}{3}$ , the probability of the event that unequal number of failures and successes occur is :

$\frac{5665}{6561}$

$\frac{6905}{6912}$

$\frac{5556}{6561}$

$\frac{5665}{6912}$

✅ Correct Option: 1

Successes $\neq$ failures means $X \neq 5$ . $P(X = 5) = \binom{10}{5}\left(\frac{1}{3}\right)^5\left(\frac{2}{3}\right)^5 = \frac{252 \times 32}{59049} = \frac{8064}{59049} = \frac{896}{6561}$ . So $P(X \neq 5) = 1 - \frac{896}{6561} = \frac{5665}{6561}$ .

2023: 11 Aug Shift 1

The probability distribution of a discrete random variable X is given by :

X	30	10	-10
P(X)	1/5	3/10	1/2

then E(X) is equals to

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If the mean of a binomial distribution is 24 and its standard deviation is 4 , then the probability of getting success is :

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In a binomial distribution the probability of getting success is $\frac{1}{4}$ And standard deviation is 3 then its mean is ?

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If the probability distribution of a random variable X is given as

$x_i$	0	1	2	3
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Then the mean of X is

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Match List - I with list- II

List-I	List - II
A. the probability distribution is applied for discrete random variable	normal distribution
B. A normal distribution is symmetric about	standard deviation
C. this probability distribution is applied for continuous random variable	mean
D. the shape of normal curve depend upon	Poisson distribution

Choose the correct option below :

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Let the random variable $X$ follow a Poisson distribution. If $P(X=3)=\dfrac{2}{5}P(X=2)$ , then $P(X=1)$ is equal to

In binomial distribution with n=10n = 10n=10 and P=13P = \frac{1}{3}P=31​, the probability of the event that unequal number of failures and successes occur is :

Solution

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CUET Mathematics Past Year Questions (Topic-Wise)

In binomial distribution with $n = 10$ and $P = \frac{1}{3}$ , the probability of the event that unequal number of failures and successes occur is :