Q 51 :

From a lot containing 10 defective and 90 non-defective bulbs, 8 bulbs are selected one by one with replacement. Then the probability of getting at least 7 defective bulbs is      [2026]

• $\frac{73}{{10}^8}$

   

• $\frac{67}{{10}^8}$

   

• $\frac{81}{{10}^8}$

   

• $\frac{7}{{10}^7}$

   

Q 52 :

The probability distribution of a random variable X is given below :

X	4k	30/7 k	32/7 k	34/7 k	36/7 k	38/7 k	40/7 k	6k
P(X)	2/15	1/15	2/15	1/5	1/15	2/15	1/5	1/15

 

If E(X) $=\frac{263}{15}$ then P(X < 20) is equal to :    [2026]

• $\frac{8}{15}$

   

• $\frac{11}{15}$

   

• $\frac{3}{5}$

   

• $\frac{14}{15}$

   

Q 53 :

Two distinct numbers $a$ and $b$ are selected at random from $1,2,3,\dots ,50$. The probability that their product $ab$ is divisible by 3, is         [2026]

• $\frac{664}{1225}$

   

• $\frac{561}{1225}$

   

• $\frac{8}{25}$

   

• $\frac{272}{1225}$

   

Q 54 :

 Let $S$ be a set of 5 elements and P(S) denote the power set of S. Let E be an event of choosing an ordered pair (A, B) from the set $P\left(S\right)\times P\left(S\right)$ such that $A\cap B=\varnothing$.  If the probability of the event E is $\frac{3^p}{2^q},$ where $p,q\in \mathrm{\mathbb{N}}$, then $p+q$ is equal to __________ .                [2026]

Q 55 :

Bag A contains 9 white and 8 black balls, while bag B contains 6 white and 4 black balls. One ball is randomly picked up from the bag B and mixed up with the balls in the bag A. Then a ball is randomly drawn from the bag A. If the probability, that the ball drawn is white, is $\frac{p}{q}$, gcd (p,q)=1, then p+q is equal to  [2026]

• 23

   

• 24

   

• 21

   

• 22

   

Q 56 :

Let n be the number obtained on rolling a fair die. If the probability that the system

$\begin{array}{c}x - ny + z = 6\\ x + (n-2)y + (n+1)z = 8\\ (n-1)y + z = 1\end{array}$ 

has a unique solution is $\frac{k}{6}$, then the sum of k and all possible values of n is: [2026]

• 20

   

• 24

   

• 21

   

• 22

   

Q 57 :

A bag contains 10 balls out of which k are red and (10−k) are black, where $0\le k\le 10$. If three balls are drawn at random without replacement and all of them are found to be black, then the probability that the bag contains 1 red and 9 black balls is:      [2026]

• $\frac{7}{110}$

   

• $\frac{7}{55}$

   

• $\frac{7}{11}$

   

• $\frac{14}{55}$