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Difficulty:
45%
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Question Stats:
67% (01:50) correct
33%
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wrong
based on 64
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A man uses a biased dice to decide whether to go ahead with a particular course of action. If the dice shows a prime number, he decided to go ahead with the course of action. What is the probability that the man goes ahead with the course of action? (The die is 6-sided with numbered from 1 to 6)
(1) The probability of the dice showing an even number is double the probability of it showing an odd number; all odd numbers are equally likely and all even numbers are also equally likely.
(2) The probability of the dice showing the number 1 is less than 1/6.
(1) The probability of the dice showing an even number is double the probability of it showing an odd number; all odd numbers are equally likely and all even numbers are also equally likely.
(2) The probability of the dice showing the number 1 is less than 1/6.
28 Oct 2025, 06:14
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Bunuel
The dice has the following set of numbers = {1,2,3,4,5,6}
The prime numbers amongst the set = {2,3,5}. If prime number comes , the man goes ahead with the course of action.
Statement 1:
(1) The probability of the dice showing an even number is double the probability of it showing an odd number; all odd numbers are equally likely and all even numbers are also equally likely.
probability of dice showing EVEN number = 2* probability of showing ODD number
p(even) = 2* p(odd)
p(even) + p(odd) = 1
P(even) = 2,4,6. Where, only 2 is a prime number.
p(even) = 3*(2*p(odd)) = 6*p(odd)
p(even) = 6 * p(odd)
p(odd) = 1,3,5, where 3 and 5 are prime numbers.
p(odd) = 3* p(odd)
P(Odd) + P(even) = 1
3* p(odd) + 6* p(odd) = 1
p(odd) = 1/9
Probability of even =2*(1/9) = 2/9
Probability of Prime = {2,3,5}
= even + Odd + Odd
= (2/9) + (1/9) + (1/9)
= 4/9
Thus, the probability of man going ahead with the course of action = (4/9).
Hence, Sufficient
Statement 2:
(2) The probability of the dice showing the number 1 is less than 1/6.
The probability of a number showing 1 is LESS THAN 1/6.
The number less than 1/6 can be any value.
Hence, Insufficient
Option A
