A man uses a biased dice to decide whether to go ahead with

Question

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.

This is a  Data Sufficiency Butler Question

Check the links to other Butler Projects:

Problem Solving Butler  
  Data Sufficiency Butler  
  Critical Reasoning Butler  
  Reading Comprehension Butler  
  Data Insights Butler

Dereno · Answer

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

ShreyaMittal1609 · Answer

The dice has the following set of numbers = {1,2,3,4,5,6}

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

Weight to each number as 1->1, 2->2, 3->1, 4->2, 5->1, 6->2
Outcome of Prime numbers= 2+1+1=4
Total outcomes= 1+2+1+2+1+2=9
Therefore, Prob of Prime numbers= 4/9

*Sufficient* - A

Adit_ · Answer

Statement 1:
Biased or not, we are having equal probability for all even and odd numbers respectively within the die albeit not being 1/6 which would be fair die case.
Since we know the relation we can calculate the exact probability for each number.
Required numbers being 2,3,5 as primes. 
Hence SUFFICIENT.

Statement 2:
Prob less than 1/6 doesnt tell us anything at all.
Clearly INSUFFICIENT.

Answer:  Option A

A man uses a biased dice to decide whether to go ahead with

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Data Sufficiency (DS) Questions

A man uses a biased dice to decide whether to go ahead with

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards