2024 Slot 1 - Two dice are thrown simultaneously. If X denotes the number of fours, then the expectation of X will be : | PYQs + Solutions

2024 Slot 1

Algebra

Medium

$\frac{5}{9}$

$\frac{1}{3}$

$\frac{4}{7}$

$\frac{3}{8}$

✅ Correct Option: 2

Related questions:

A die is rolled thrice. What is the probability of getting a number greater than $4$ in the first and the second throw of dice and a number less than $4$ in the third throw ?

If the random variable $X$ has the following distribution:

$ X $	0	1	2	otherwise
$P(X)$	$k$	$2k$	$3k$	$0$

Match List-I with List-II:

List-I	List-II
(A) $k$	(I) $\frac{5}{6}$
(B) $P(X < 2)$	(II) $\frac{4}{3}$
(C) $E(X)$	(III) $\frac{1}{2}$
(D) $P(1 \leq X \leq 2)$	(IV) $\frac{1}{6}$

Let $X$ denote the number of hours you play during a randomly selected day. The probability that $X$ can take values $x$ has the following form, where $c$ is some constant.

$\mathrm{P}(\mathrm{X}=\mathrm{x})=\left\{\begin{array}{lll} 0.1, & \text { if } \mathrm{x}=0 \\ \mathrm{cx}, & \text { if } \mathrm{x}=1 \text { or } \mathrm{x}=2 \\ \mathrm{c}(5-\mathrm{x}), & \text { if } \mathrm{x}=3 \text { or } \mathrm{x}=4 \\ 0, & \text { otherwise } \end{array}\right.$

Match List-I with List-II :

List-I	List-II
(A) $c$	(I) 0.75
(B) $P(X \leq 2)$	(II) 0.3
(C) $P(X = 2)$	(III) 0.55
(D) $P(X \geq 2)$	(IV) 0.15

2024 Slot 1 PYQs

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