(A) The total number of cards is $52$. The number of spade cards is $13$.Probability of drawing a spade in one draw,$P(S) = \frac{13}{52} = \frac{1}{4

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(A) The total number of cards is $52$. The number of spade cards is $13$.Probability of drawing a spade in one draw,$P(S) = \frac{13}{52} = \frac{1}{4}$.Probability of not drawing a spade in one draw,$P(S') = 1 - \frac{1}{4} = \frac{3}{4}$.Since the card is replaced each time,the events are independent.The probability that he fails the first two times means he does not get a spade in the first draw $AND$ he does not get a spade in the second draw.Required probability $= P(S') \times P(S') = \frac{3}{4} \times \frac{3}{4} = \frac{9}{16}$.

Class 12 Mathematics Probability Probability distribution

Medium

$A$ man draws a card from a pack of $52$ playing cards,replaces it,and shuffles the pack. He continues this process until he gets a spade card. The probability that he will fail the first two times is:

A
$\frac{9}{16}$
B
$\frac{1}{16}$
C
$\frac{9}{64}$
D
None of these

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Probability

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Probability distribution

$A$ random variable $X$ has the probability distribution as shown below. For the events $E = \{ X \text{ is a prime number} \}$ and $F = \{ X < 4 \}$,the probability $P(E \cup F)$ is:

$X$ $1$ $2$ $3$ $4$ $5$ $6$ $7$ $8$

$P(X)$ $0.15$ $0.23$ $0.12$ $0.10$ $0.20$ $0.08$ $0.07$ $0.05$

MediumAIEEE 2004

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Let $X$ be the discrete random variable representing the number $(x)$ that appears on the face of a biased die when it is rolled. The probability distribution of $X$ is given by:
$X = x$ $1$ $2$ $3$ $4$ $5$ $6$
$P(X = x)$ $0.1$ $0.15$ $0.3$ $0.25$ $k$ $k$

Find the variance of $X$.

MediumTS EAMCET 2020

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$A$ person throws an unbiased die. If the number shown is even,he gains an amount equal to the number shown. If the number is odd,he loses an amount equal to the number shown. Then his expectation is ₹.

EasyMHT CET 2024

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If the probability mass function (p.m.f.) of a random variable $X$ is $P(X=x) = \frac{1}{10}$ for $x = 1, 2, 3, \ldots, 10$,and $0$ otherwise,then $\operatorname{Var}(X)$ is equal to:

EasyMHT CET 2022

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Suppose the number of accidents occurring on a highway in each day follows a Poisson random variable with parameter $3$. Then,what is the probability that no accidents occur today?

DifficultAP EAMCET 2020

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$X$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$
$P(X)$	$0.15$	$0.23$	$0.12$	$0.10$	$0.20$	$0.08$	$0.07$	$0.05$

$X = x$	$1$	$2$	$3$	$4$	$5$	$6$
$P(X = x)$	$0.1$	$0.15$	$0.3$	$0.25$	$k$	$k$

$A$ man draws a card from a pack of $52$ playing cards,replaces it,and shuffles the pack. He continues this process until he gets a spade card. The probability that he will fail the first two times is:

Similar Questions

$A$ random variable $X$ has the probability distribution as shown below. For the events $E = \{ X \text{ is a prime number} \}$ and $F = \{ X < 4 \}$,the probability $P(E \cup F)$ is: $X$ $1$ $2$ $3$ $4$ $5$ $6$ $7$ $8$ $P(X)$ $0.15$ $0.23$ $0.12$ $0.10$ $0.20$ $0.08$ $0.07$ $0.05$

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$A$ random variable $X$ has the probability distribution as shown below. For the events $E = \{ X \text{ is a prime number} \}$ and $F = \{ X < 4 \}$,the probability $P(E \cup F)$ is:

$X$ $1$ $2$ $3$ $4$ $5$ $6$ $7$ $8$

$P(X)$ $0.15$ $0.23$ $0.12$ $0.10$ $0.20$ $0.08$ $0.07$ $0.05$

Let $X$ be the discrete random variable representing the number $(x)$ that appears on the face of a biased die when it is rolled. The probability distribution of $X$ is given by:
$X = x$ $1$ $2$ $3$ $4$ $5$ $6$
$P(X = x)$ $0.1$ $0.15$ $0.3$ $0.25$ $k$ $k$

Find the variance of $X$.