Rachel is throwing a die with sides numbered consecutively from 1 to x. What is the probability that she gets at least one x?
(1) The probability of getting an x on either of the two times that Rachel throws the die is 1/5.
(2) If Rachel had thrown the die one more time, the probability of getting at least one x would have been 61/125.
please help!
thanks!
Probability: Princeton Review Diagnostic
This topic has expert replies
- GMATGuruNY
- GMAT Instructor
- Posts: 15539
- Joined: Tue May 25, 2010 12:04 pm
- Location: New York, NY
- Thanked: 13060 times
- Followed by:1906 members
- GMAT Score:790
P(at least one x) = 1 - P(no x's).tpz wrote:Rachel is throwing a die with sides numbered consecutively from 1 to x. What is the probability that she gets at least one x?
(1) The probability of getting an x on either of the two times that Rachel throws the die is 1/5.
(2) If Rachel had thrown the die one more time, the probability of getting at least one x would have been 61/125.
Statement 1: The probability of getting an x on either of THE TWO TIMES that Rachel throws the die is 1/5.
The die is being thrown TWO TIMES.
Since P(x) = 1/5, P(not x) = 4/5.
Thus, P(no x's) = 4/5 * 4/5 = 16/25.
Thus, P(at least one x) = 1 - 16/25 = 9/25.
SUFFICIENT.
Statement 2: If Rachel had thrown the die one more time, the probability of getting at least one x would have been 61/125.
For the correct answer to be D, statement 2 must offer the SAME TWO FACTS as statement 1:
Fact 1: The die is thrown two times (implying that ONE MORE TIME = THREE throws).
Fact 2: P(x) = 1/5.
Check whether these two facts satisfy statement 2:
P(not X on each of 3 throws) = 4/5 * 4/5 * 4/5 = 64/125.
P(at least one x) = 1 - 64/125 = 61/125.
Success!,
Since P(x) = 1/5 and a total three throws constitute the ONLY combination that will yield a result of 61/125, we know that statement 2 offers the SAME TWO FACTS as statement 1, implying that Rachel actually throws the die TWO TIMES and that P(at least one x) = 9/25.
SUFFICIENT.
The correct answer is D.
Private tutor exclusively for the GMAT and GRE, with over 20 years of experience.
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.
As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.
For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
Student Review #2
Student Review #3
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.
As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.
For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
Student Review #2
Student Review #3