CUET UG Mathematics Applied Mathematics Probability Previous Year Question Paper and Solution with PDF

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CUET UG Mathematics Applied Mathematics
Previous Year Questions

CUET UG Mathematics Applied Mathematics
Previous Year Questions
CUET UG Mathematics Applied Mathematics

CUET UG Mathematics Applied Mathematics Previous Year Questions (PYQs)

CUET UG Mathematics Applied Mathematics Probability PYQ

Qus : 1 CUET UG Mathematics Applied Mathematics PYQ

Two dice are thrown simultaneously. If X denotes the number of fours, then the expectation of X will be:

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CUET UG Mathematics Applied Mathematics Previous Year PYQ CUET UG Mathematics Applied Mathematics CUET UG 2024 Mathematics PYQ

Solution

Qus : 2 CUET UG Mathematics Applied Mathematics PYQ

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

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

Match List-I with List-II :

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

Choose the correct answer from the options given below :

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CUET UG Mathematics Applied Mathematics Previous Year PYQ CUET UG Mathematics Applied Mathematics CUET UG 2024 Mathematics PYQ

Solution

Qus : 3 CUET UG Mathematics Applied Mathematics PYQ

For two events $A, B$

$P(A\cup B)=\frac{7}{12}, ; P(A)=\frac{5}{12}, ; P(B)=\frac{3}{12}$

Then $P(A\cap B)=$

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CUET UG Mathematics Applied Mathematics Previous Year PYQ CUET UG Mathematics Applied Mathematics CUET UG 2022 Applied Mathematics PYQ

Solution

We know,

$P(A\cup B)=P(A)+P(B)-P(A\cap B)$

Substitute values:

$\frac{7}{12}=\frac{5}{12}+\frac{3}{12}-P(A\cap B)$

$\frac{7}{12}=\frac{8}{12}-P(A\cap B)$

So,

$P(A\cap B)=\frac{8}{12}-\frac{7}{12}$

$=\frac{1}{12}$

Qus : 4 CUET UG Mathematics Applied Mathematics PYQ

In a game, a child will win Rs $5$ if he gets all heads or all tails when three coins are tossed simultaneously and he will lose Rs $3$ for all other cases.

The expected amount to lose in the game is:

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CUET UG Mathematics Applied Mathematics Previous Year PYQ CUET UG Mathematics Applied Mathematics CUET UG 2022 Applied Mathematics PYQ

Solution

Total outcomes when 3 coins tossed:

$2^3=8$

Favourable (all heads or all tails):

HHH, TTT → 2 outcomes

So,

$P(\text{win})=\frac{2}{8}=\frac{1}{4}$

$P(\text{lose})=\frac{6}{8}=\frac{3}{4}$

Expected value:

$E=5\left(\frac{1}{4}\right)+(-3)\left(\frac{3}{4}\right)$

$=\frac{5}{4}-\frac{9}{4}$

$=-\frac{4}{4}$

$=-1$

So expected loss = Rs. 1

Qus : 5 CUET UG Mathematics Applied Mathematics PYQ

If events $A$ and $B$ are independent, then identify the correct statements

(A) $A$ and $B$ must be mutually exclusive

(B) The sum of their probabilities must be equal to $1$

(D) $A'$ and $B'$ are also independent

Choose the correct answer from the options given below:

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CUET UG Mathematics Applied Mathematics Previous Year PYQ CUET UG Mathematics Applied Mathematics CUET UG 2022 Applied Mathematics PYQ

Solution

For independent events

$P(A\cap B)=P(A)P(B)$

So statement (C) is **true**.

Independent events need not be mutually exclusive.

Therefore (A) is **false**.

Also $P(A)+P(B)$ need not be $1$.

Hence (B) is **false**.

If $A$ and $B$ are independent then their complements $A'$ and $B'$ are also independent.

Hence (D) is **true**.

Correct statements: **C and D**

Qus : 6 CUET UG Mathematics Applied Mathematics PYQ

If $A$ and $B$ are two independent events with

$P(A)=\frac{3}{5}$ and $P(B)=\frac{4}{9}$, then

$P(A' \cap B')$ is equal to

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CUET UG Mathematics Applied Mathematics Previous Year PYQ CUET UG Mathematics Applied Mathematics CUET UG 2022 Applied Mathematics PYQ

Solution

Since $A$ and $B$ are independent,

$P(A\cap B)=P(A)P(B)$

Now

$P(A') = 1 - P(A)$

$P(B') = 1 - P(B)$

$P(A') = 1-\frac{3}{5}=\frac{2}{5}$

$P(B') = 1-\frac{4}{9}=\frac{5}{9}$

For independent events, complements are also independent.

Hence

$P(A'\cap B') = P(A')P(B')$

$=\frac{2}{5}\times\frac{5}{9}$

$=\frac{2}{9}$

Qus : 7 CUET UG Mathematics Applied Mathematics PYQ

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

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CUET UG Mathematics Applied Mathematics Previous Year PYQ CUET UG Mathematics Applied Mathematics CUET UG 2024 Mathematics PYQ