In a drawer of shirts, 8 are blue, 6 are green, and 4 are magenta.

Question

In a drawer of shirts, 8 are blue, 6 are green, and 4 are magenta. If Mason draws 2 shirts at random, what is the probability that at least one of the shirts he draws will be blue?

A. 25/153
B. 28/153
C. 5/17
D. 4/9
E. 12/17

This is a  PS Butler Question

Check the links to other Butler Projects:

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

aditya1818 · Answer

In a drawer of shirts, 8 are blue, 6 are green, and 4 are magenta. If Mason draws 2 shirts at random, what is the probability that at least one of the shirts he draws will be blue?

Whenever you see a atleast condition immediately apply (Total - None condition)

So condition when no blue ball is picked = 10C2
and total ways to pick total any 2 balls out of 18 = 18C2

So our answer
 1- (10C2 / 18C2)
= 12/17

ravi1522 · Answer

Hello,
In a drawer of shirts, 8 are blue, 6 are green, and 4 are magenta. If Mason draws 2 shirts at random, what is the probability that at least one of the shirts he draws will be blue?

probability of at least one blue can be calculated by 1- probability of no blue
=1-(10C2/18C2)
1-(5/17)
so 12/17
Hence answer is E

Dereno · Answer

Total dresses in the cupboard = 8 Blue + 6 Green + 4 Magenta = 8+6+4 = 18

Mason draws 2 dresses from the cupboard.

Probability (Atleast one blue ) = ?

= 1 - Probability ( No Blues)

= 1 - (10C2 / 18 C2)

As , we remove the blues from total. We are left with 18-8 = 10 dresses which are not blue.

= 1 -

= 1 - (10/34)

=  12/17

Option E

Alternate method  :

At least ONE Blue = ( Blue and green) + ( Blue and Magenta ) + (2 blues)

= (8C1*6C1) / (18C2) + (8C1*4C1) / (18C2) + (8C2) / (18C2)

= (48+32+28)/(9*17)

= 108/153

=  12/17

Option E

007Phoenix007 · Answer

For getting the probability of choosing atleast 1 blue, the easy method is to subtract the probability of no blue from 1
Therefore:
Atleast 1 blue= 1- prob(no blue)
= 1- (10C2/18C2)
= 1- (10×9/(18×17))
= 1- 5/17
= 12/17

Option E is correct

In a drawer of shirts, 8 are blue, 6 are green, and 4 are magenta.

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 Problem Solving (PS) Questions

In a drawer of shirts, 8 are blue, 6 are green, and 4 are magenta.

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