CAT 2025 Lesson : Class Discussion: Modern Maths - Probability: 9 to 16

CLASS DISCUSSION - Probability

Question 9

A, B, C and D have one chance to hit the target. The probabilities of the 4 of them hitting the targets are 0.1, 0.2, 0.4 and 0.5 respectively. What is the probability (as %) of at least one of them hitting the target (rounded to the nearest integer)?

Answer: 78

Question 10

In a private club, a total of 100 lottery tickets are sold. Exactly ten of these tickets would be declared the winning tickets. Kamali purchased two of these lottery tickets. What is the probability that at least 1 of the winning tickets is held by Kamali, as a percentage rounded to the nearest integer?

Answer: 19

Question 11

A box contains 6 cricket balls, 5 tennis balls and 4 rubber balls. Of these, some balls are defective. The proportion of defective cricket balls is more than the proportion of defective tennis balls but less than the proportion of defective rubber balls. Moreover, the overall proportion of defective balls is twice the proportion of defective tennis balls. What BEST can be said about the number of defective rubber balls in the box?
[XAT 2020]

		It is exactly 2
		It is exactly 3
		It is either 2 or 3
		It is either 0 or 1
		It is either 3 or 4

Question 12

What is the probability that the sum of the numbers on three dice that have been rolled is 10?

		$\dfrac{1}{6}$
		$\dfrac{1}{8}$
		$\dfrac{1}{12}$
		None of the above

Question 13

The odds against CSK defeating RCB in a match is 1 to 3. If a 5-match series is played between CSK and RCB, then what is the probability of RCB winning the series as a percentage (round it to the nearest integer)? [Note that all matches are won by a team, i.e., none of the matches end in a draw or a tie]

Answer: 10

Question 14

A bag contains 4 red pens and 6 black pens. Chitra is required to pick a pen from the bag and state its colour. She speaks the truth only 60% of the time. If she picked two pens one after the other without replacement, and stated the colour as red both the times, then what is the probability that both the pens are of the same colour?

		$\dfrac{9}{43}$
		$\dfrac{19}{43}$
		$\dfrac{29}{43}$
		None of the above

Question 15

Ashok has a bag containing 40 cards, numbered with the integers from 1 to 40. No two cards are numbered with the same integer. Likewise, his sister Shilpa has another bag containing only five cards that are numbered with the integers from 1 to 5, with no integer repeating. Their mother, Latha, randomly draws one card each from Ashok’s and Shilpa’s bags and notes down their respective numbers. If Latha divides the number obtained from Ashok’s bag by the number obtained from Shilpa’s, what is the probability that the remainder will not be greater than 2?
[XAT 2020]

		0.73
		0.8
		0.87
		0.91
		0.94

Question 16

There are eight different blood types. In a hospital there are 5 babies born on a given day. The nurse noted down the blood types of the 5 babies. What is the probability that the nurse wrote down exactly 2 different blood types?

		$\dfrac{35}{1024}$
		$\dfrac{75}{2048}$
		$\dfrac{7}{512}$
		$\dfrac{105}{4096}$

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