CAT 2025 Lesson : Probability - Past Questions

Question 1

The probability that in a household LPG will last 60 days or more is 0.8 and that it will last at most 90 days is 0.6. The probability that the LPG will last 60 to 90 days is
[IIFT 2012]

		$0.40$
		$0.50$
		$0.75$
		None of the above

Answer: (1)

0.40

Question 2

There are four machines in a factory. At exactly 8 pm, when the mechanic is about to leave the factory, he is informed that two of the four machines are not working properly. The mechanic is in a hurry, and decides that he will identify the two faulty machines before going home, and repair them next morning. It takes him twenty minutes to walk to the bus stop. The last bus leaves at 8:32 pm. If it takes six minutes to identify whether a machine is defective or not, and if he decides to check the machines at random, what is the probability that the mechanic will be able to catch the last bus?
[XAT 2011]

		$0$
		$\dfrac{1}{6}$
		$\dfrac{1}{4}$
		$\dfrac{1}{3}$
		$1$

Answer: (4)

\dfrac{1}{3}

Question 3

Aditya has a total of 18 red and blue marbles in two bags (each bag has marbles of both colors). A marble is randomly drawn from the first bag followed by another randomly drawn from the second bag. The probability of both being red is 5/16. What is the probability of both marbles being blue?
[XAT 2014]

		$\dfrac{1}{16}$
		$\dfrac{2}{16}$
		$\dfrac{3}{16}$
		$\dfrac{4}{16}$
		None of the above

Answer: (3)

\dfrac{3}{16}

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