GRE Prep Club Daily Prep
Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.
Customized
for You
Track
Your Progress
Practice
Pays
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
What is the probability of rolling a number less than 3 at l
[#permalink]
13 Aug 2020, 01:59
13 Aug 2020, 01:59
Expert Reply
15
Bookmarks
00:00
Question Stats:
52% (02:55) correct
47% (02:54) wrong based on 63 sessions
Hide Show timer Statistics
What is the probability of rolling a number less than 3 at least 3 times in 5 rolls of a six-sided die?
A. 2/15
B. 17/81
C. 1/3
D. 2/5
E. 15/32
KUDOS for the right solution and explanation
A. 2/15
B. 17/81
C. 1/3
D. 2/5
E. 15/32
KUDOS for the right solution and explanation
Re: What is the probability of rolling a number less than 3 at l
[#permalink]
13 Aug 2020, 16:35
13 Aug 2020, 16:35
4
3
Bookmarks
p= probability of rolling a number less than 3 = 2/6 =1/3
(namely rolling a 1 or 2 out of the 6 numbers)
Therefore
1-p= probability of not rolling a number less than 3 = 1-(1/3)= 2/3
Using Binomial Distribution
Case 1: Rolling a number less than 3 three times
(5 choose 3)*(p)^3*(1-p)^5-3= 5!/(2!3!) * (1/3)^3 * (2/3)^2 = 10(4/243) = 40/243
Case 2: Rolling a number less than 3 four times
(5 choose 4)*p^4 *(1-p)^5-4= 5!/(1!4!) * (1/3)^4 * (2/3)^1 = 5(2/243) = 10/243
Case 3: Rolling a number less than 3 five times
(5 choose 5)* p^5*(1-p)^0 = 5!/(0!5!)* (1/3)^5 * (2/3)^0 = 1*(1/243)(1)= 1/243
We add the probabilities of all the cases to get
40/243+ 10/243+ 1/243 = 51/243 = 17/81
Final Answer: B
(namely rolling a 1 or 2 out of the 6 numbers)
Therefore
1-p= probability of not rolling a number less than 3 = 1-(1/3)= 2/3
Using Binomial Distribution
Case 1: Rolling a number less than 3 three times
(5 choose 3)*(p)^3*(1-p)^5-3= 5!/(2!3!) * (1/3)^3 * (2/3)^2 = 10(4/243) = 40/243
Case 2: Rolling a number less than 3 four times
(5 choose 4)*p^4 *(1-p)^5-4= 5!/(1!4!) * (1/3)^4 * (2/3)^1 = 5(2/243) = 10/243
Case 3: Rolling a number less than 3 five times
(5 choose 5)* p^5*(1-p)^0 = 5!/(0!5!)* (1/3)^5 * (2/3)^0 = 1*(1/243)(1)= 1/243
We add the probabilities of all the cases to get
40/243+ 10/243+ 1/243 = 51/243 = 17/81
Final Answer: B
General Discussion
Re: What is the probability of rolling a number less than 3 at l
[#permalink]
15 Aug 2020, 04:07
15 Aug 2020, 04:07
1
Bookmarks
Carcass wrote:
What is the probability of rolling a number less than 3 at least 3 times in 5 rolls of a six-sided die?
A. 2/15
B. 17/81
C. 1/3
D. 2/5
E. 15/32
KUDOS for the right solution and explanation
A. 2/15
B. 17/81
C. 1/3
D. 2/5
E. 15/32
KUDOS for the right solution and explanation
@carcass can we solve this question using complement rule ??? if ues kindly show the solution in this way
