Raffle tickets numbered consecutively from 101 through 350 are placed in a box. What is the probability that a ticket selected at random will have a number with a hundreds digit of 2?
A) 2/5
B) 2/7
C) 33/83
D) 99/250
E) 100/249
Rich and Ankur have provided nice solutions, so I won't solve the question again.
However, I do want to add a
pro tip to remember when answering questions using calculating probabilities using the formula:
P(event A occurs) = (# of outcomes where event A occurs)/(total # of outcomes)
In these cases,
calculate the denominator first
There are two reasons for this:
1) The denominator is usually the easier value to calculate
2) If you can't calculate the numerator, you can probably use the denominator to eliminate answer choices.
Here's what I mean:
In this question, P(number has a hundreds digit of 2) = (
# of integers with hundreds digit of 2)/(
# of integers to choose from)
# of integers to choose from = 350 - 101 + 1 =
250
So, P(number has a hundreds digit of 2) =
??)/(
250)
This tells us that the correct answer EITHER has
250 in its denominator OR, when the probability is simplified, the new denominator is a factor of
250
At this point, if we can't calculate the numerator, we eliminate some answer choices
A) 2/5
[5 is a factor of 250, so this answer COULD be correct]
B) 2/7
[7 is NOT a factor of 250. ELIMINATE B]
C) 33/83
[83 is NOT a factor of 250. ELIMINATE C]
D) 99/250
[250 is a factor of 250, so this answer COULD be correct]
E) 100/249
[249 is NOT a factor of 250. ELIMINATE E]
So, we were able to deduce that the correct answer is either A or D.
For more on this concept, see the following videos:
- Introduction to Probability:
https://www.gmatprepnow.com/module/gmat ... /video/742
- General Probability Strategies:
https://www.gmatprepnow.com/module/gmat ... /video/757
Cheers,
Brent
