Probability - Algebra - Mathematics Previous Year Questions

1

2024 · Mathematics · Algebra · Probability

TG EAPCET 2024 ONLINE 10TH MAY EVENING SHIFT

The probability that exactly 3 heads appear in six tosses of an unbiased coin, given that first three tosses resulted in 2 or more heads is

A

$\frac{3}{16}$

B

$\frac{5}{16}$

C

$\frac{1}{4}$

D

$\frac{9}{16}$

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2

2024 · Mathematics · Algebra · Probability

TG EAPCET 2024 ONLINE 10TH MAY EVENING SHIFT

A student has to write the words ABILITY, PROBABILITY, FACILITY, MOBILITY. He wrote one word and erased all the letters in it except two consecutive letters. If 'LI' is left after erasing then the probability that the boy wrote the word PROBABILITY is

A

$\frac{21}{116}$

B

$\frac{72}{116}$

C

$\frac{3}{5}$

D

$\frac{2}{3}$

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3

2024 · Mathematics · Algebra · Probability

TG EAPCET 2024 ONLINE 10TH MAY EVENING SHIFT

Two cards are drawn at random one after the other with replacement from a pack of playing cards. If $X$ is the random variable denoting the number of ace cards drawn, then the mean of the probability distribution of X is

A

2

B

$\frac{2}{13}$

C

1

D

$\frac{1}{13}$

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4

2024 · Mathematics · Algebra · Probability

TG EAPCET 2024 ONLINE 10TH MAY EVENING SHIFT

If three numbers are randomly selected from the set $\{1,2,3, \ldots \ldots 50\}$, then the probability that they are in arithmetic progression is

A

$\frac{3}{50}$

B

$\frac{3}{98}$

C

$\frac{3}{49}$

D

$\frac{3}{25}$

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5

2024 · Mathematics · Algebra · Probability

TG EAPCET 2024 ONLINE 10TH MAY MORNING SHIFT

Bag $P$ contains 3 white, 2 red, 5 blue balls and bag $Q$ contains 2 white, 3 red, 5 blue balls. A ball is chosen at random from $P$ and is placed in $Q$. If a ball is chosen from bag $Q$ at random, then the probability that it is a red ball is

A

$\frac{9}{50}$

B

$\frac{13}{45}$

C

$\frac{16}{55}$

D

$\frac{12}{35}$

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6

2024 · Mathematics · Algebra · Probability

TG EAPCET 2024 ONLINE 10TH MAY MORNING SHIFT

If the probability distribution of a random variable $X$ is as follow, then the variance of $X$ is

$X=x$	2	3	5	9
$P(X=x)$	$k$	$2 k$	$3 k^2$	$k$

A

$\frac{61}{4}$

B

$\frac{7}{2}$

C

12

D

3

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7

2024 · Mathematics · Algebra · Probability

TG EAPCET 2024 ONLINE 10TH MAY MORNING SHIFT

If two dice are thrown, then the probability of getting co-prime numbers on the dice is

A

$\frac{23}{36}$

B

$\frac{13}{36}$

C

$\frac{5}{6}$

D

$\frac{1}{6}$

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8

2024 · Mathematics · Algebra · Probability

TG EAPCET 2024 ONLINE 10TH MAY MORNING SHIFT

If two cards are drawn at random simultaneously from a well shuffled pack of 52 playing cards, then the probability of getting a cards having a composite number and a card having a number which is a multiple of 3 is

A

$\frac{94}{663}$

B

$\frac{62}{663}$

C

$\frac{102}{663}$

D

$\frac{64}{663}$

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9

2024 · Mathematics · Algebra · Probability

TG EAPCET 2024 ONLINE 11TH MAY MORNING SHIFT

If a random variable $X$ has the following probability distribution, then its variance is

X = x	1	3	5	2
P(X = x)	$3 K^2$	K	$K^2$	2K

A

$\frac{9}{4}$

B

$\frac{25}{8}$

C

$\frac{27}{16}$

D

$\frac{15}{16}$

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10

2024 · Mathematics · Algebra · Probability

TG EAPCET 2024 ONLINE 11TH MAY MORNING SHIFT

The numbers $2,3,5,7,11,13$ are written on six distinct paper chits. If 3 of them are chosen at random, then the probability that the sum of the numbers on the obtained chits is divisible by 3 , is

A

$\frac{7}{20}$

B

$\frac{6}{20}$

C

$\frac{5}{20}$

D

$\frac{1}{5}$

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11

2024 · Mathematics · Algebra · Probability

TG EAPCET 2024 ONLINE 11TH MAY MORNING SHIFT

If two dice are rolled, then the probability of getting a multiple of 3 as the sum of the numbers appeared on the top faces of the dice, if it is known that their sum is an odd number, is

A

$\frac{1}{6}$

B

$\frac{11}{36}$

C

$\frac{1}{3}$

D

$\frac{7}{18}$

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12

2024 · Mathematics · Algebra · Probability

TG EAPCET 2024 ONLINE 11TH MAY MORNING SHIFT

The mean and variance of a binomial variate $X$ are $\frac{16}{5}$ and $\frac{48}{25}$ respectively. IfP $(X > 1)=1-K\left(\frac{3}{5}\right)^{7}$, then $5 K=$

A

19

B

3

C

2

D

11

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13

2024 · Mathematics · Algebra · Probability

TG EAPCET 2024 ONLINE 9TH MAY EVENING SHIFT

If 3 dice are thrown, the probability of getting 10 as the sum of the three numbers that appeared on the top faces of the dice is

A

$\frac{1}{9}$

B

$\frac{7}{72}$

C

$\frac{5}{36}$

D

$\frac{1}{8}$

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14

2024 · Mathematics · Algebra · Probability

TG EAPCET 2024 ONLINE 9TH MAY EVENING SHIFT

Three similar urns $A, B, C$ contain 2 red and 3 white balls; 3 red and 2 white balls; 1 red and 4 white balls respectively. If a ball selected at random from one of the urns is found to be red, then the probability that it is drawn from urn $C$ is

A

$\frac{1}{6}$

B

$\frac{1}{3}$

C

$\frac{1}{2}$

D

$\frac{2}{9}$

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15

2024 · Mathematics · Algebra · Probability

TG EAPCET 2024 ONLINE 9TH MAY EVENING SHIFT

Among the 5 married couples, if the names of 5 men are matched with the names of their wives randomly, then the probability that no man is matched with name of his wife is

A

$\frac{9}{20}$

B

$\frac{1}{5}$

C

$\frac{11}{30}$

D

$\frac{17}{60}$

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16

2024 · Mathematics · Algebra · Probability

TG EAPCET 2024 ONLINE 9TH MAY EVENING SHIFT

A A fair coin is tossed a fixed number of times. If the probability of getting 5 heads is equal to the probability of getting 4 heads, then the probability of getting 6 heads is

A

$\frac{7}{64}$

B

$\frac{9}{32}$

C

$\frac{21}{128}$

D

$\frac{35}{256}$

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17

2024 · Mathematics · Algebra · Probability

TG EAPCET 2024 ONLINE 9TH MAY EVENING SHIFT

If a random variable X has the following probability distribution, then the mean of $X$ is \(\begin{array}{c|c|c|c|c} X=x_1 & 1 & 2 & 3 & 5 \\ \[\hline p\left(X=x_i\right) & 2 k^2 & k & k & k^2\] \end{array}\)

A

$\frac{26}{9}$

B

$\frac{22}{9}$

C

$\frac{24}{9}$

D

$\frac{28}{9}$

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18

2025 · Mathematics · Algebra · Probability

TG EAPCET 2025 ONLINE 2ND MAY EVENING SHIFT

$A, B_1, B_2, B_3$ are the events in a random experiment. If $P\left(B_1\right)=0.25, P\left(B_2\right)=0.30, P\left(B_3\right)=0.45, P\left(\frac{A}{B_1}\right)=0.05$, $P\left(\frac{A}{B_2}\right)=0.04, P\left(\frac{A}{B_3}\right)=0.03$, then $P\left(\frac{B_2}{A}\right)=$

A

$\frac{6}{19}$

B

$\frac{8}{19}$

C

$\frac{12}{19}$

D

$\frac{5}{19}$

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19

2025 · Mathematics · Algebra · Probability

TG EAPCET 2025 ONLINE 2ND MAY EVENING SHIFT

A typist claims that he prepares a typed page with typo errors of 1 per 10 pages. In a typing assignment of 40 pages, if the probability that the typo errors are at most 2 is $p$, then $e^2 p=$

A

5

B

13

C

$13 e^{-2}$

D

$5 e^{-2}$

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20

2025 · Mathematics · Algebra · Probability

TG EAPCET 2025 ONLINE 2ND MAY EVENING SHIFT

$A, B$ are the events in a random experiment.

If $P(A)=\frac{1}{2}, P(B)=\frac{1}{3}, P(A \cap B)=\frac{1}{4}$, then $P\left(\frac{A^c}{B^c}\right)+P\left(\frac{A}{B}\right)=$

A

1

B

$\frac{4}{5}$

C

$\frac{11}{8}$

D

$\frac{7}{3}$

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