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What is the probability of rolling a number less than 3 at l
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13 Aug 2020, 01:59
13 Aug 2020, 01:59
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Question Stats:
57% (02:59) correct
42% (02:53) wrong based on 77 sessions
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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
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13 Aug 2020, 16:35
13 Aug 2020, 16:35
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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
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15 Aug 2020, 04:07
15 Aug 2020, 04:07
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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
