Modern Math - Probability - Previous Year CAT/MBA Questions
The best way to prepare for Modern Math - Probability is by going through the previous year Modern Math - Probability CAT questions. Here we bring you all previous year Modern Math - Probability CAT questions along with detailed solutions.
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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?
- (a)
- (b)
- (c)
- (d)
None of these
Answer: Option A
Text Explanation :
Total number of four-digit numbers that can be formed = 4!.
If the number is divisible by 25, then the last two digits are 25.
So the first two digits can be arranged in 2! ways.
Hence, required probability =
Workspace:
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: 2
Text Explanation :
53 Sundays can occur in a non-leap year, if 1st January is either a Saturday or a Sunday. But 54 Sundays can never occur.
Hence, I < II.
Workspace:
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
- (a)
1/18
- (b)
1/3
- (c)
1/6
- (d)
2/3
Answer: Option C
Text Explanation :
Since there are 6 red balls and all six of them are of different sizes, probability of choosing the smallest among them is .
Hence, option (c).
Workspace:
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?
- (a)
Rs. 2.50
- (b)
Rs. 2
- (c)
Rs. 3.50
- (d)
Rs. 4
Answer: Option A
Text Explanation :
Since in the long run the probability of each number appearing is the same, we can say in ‘n’ throws one can get 1, 2, 3, 4, 5 and 6, n/6 times each.
Hence he would earn (1 + 2 + 3 + 4 + 5 + 6)n/6 = Rs. 7n/2 = Rs. 3.5n.
∴ His average earning for each through is 3.5n/n = Rs. 3.5
In order to make a profit of 1 Re. per throw his cost for the each through should be = 3.5 – 1 = Rs. 2.50
Hence, option (a).
Workspace:
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