Probability — CAT Previous-Year Questions
4 previous-year questions on Probability from CAT, with full solutions. Practise free — check answers as you go; sign in to save your progress.
Probability · CAT PYQs
Direction: Answer the questions based on the following information.
Four sisters — Suvarna, Tara, Uma and Vibha are playing a game such that the loser doubles the money of each of the other players from her share. They played four games and each sister lost one game in alphabetical order. At the end of fourth game, each sister had Rs.32.
If a 4 digit number is formed with digits 1, 2, 3 and 5. What is the probability that the number is divisible by 25, if repetition of digits is not allowed?
Answer the next 3 questions based on the information given below:
Alphonso, on his death bed, keeps half his property for his wife and divide the rest equally among his three sons Ben, Carl and Dave. Some years later Ben dies leaving half his property to his widow and half to his brothers Carl and Dave together, shared equally. When Carl makes his will he keeps half his property for his widow and the rest he bequeaths to his younger brother Dave. When Dave dies some years later, he keeps half his property for his widow and the remaining for his mother. The mother now has Rs. 1,575,000.
Data is provided followed by two statements – I and II – both resulting in a value, say I and II.
As your answer,
Type 1, if I > II.
Type 2, if I < II.
Type 3, if I = II.
Type 4, if nothing can be said.
I. The probability of encountering 54 Sundays in a leap year.
II. The probability of encountering 53 Sundays in a non-leap year.
Answer the next 2 questions based on the information given below:
A function f(x) is said to be even if f(–x) = f(x), and odd if f(–x) = –f(x). Thus, for example, the function given by f(x) = x2 is even, while the function given by f(x) = x3 is odd. Using this definition, answer the following questions.
A box contains 6 red balls, 7 green balls and 5 blue balls. Each ball is of a different size. The probability that the red ball selected is the smallest red ball, is
Answer the following questions based on the information given below:
There were a hundred schools in a town. Of these, the number of schools having a play – ground was 30, and these schools had neither a library nor a laboratory. The number of schools having a laboratory alone was twice the number of those having a library only. The number of schools having a laboratory as well as a library was one fourth the number of those having a laboratory alone. The number of schools having either a laboratory or a library or both was 35.
A player rolls a die and receives the same number of rupees as the number of dots on the face that turns up. What should the player pay for each roll if he wants to make a profit of one rupee per throw of the die in the long run?