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D
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For one roll of a certain die, the probability of rolling a two is 1/6. If this die is rolled
4 times, which of the following is the probability that the outcome will be a two at
least 3 times?
(A) (1/6)4
(8) 2(1/6i + (1/6)4
(C) 3{1/6)3(5/6) + (1/6)4
(O) 4{1/6)3{5/6) + (1/6)4
(E) 6{1/6)3{5/6) + (1/6)4
Corrected options:
(A) (1/6)^4
(B) 2(1/6)^3 + (1/6)^4
(C) 3(1/6)^3(5/6) + (1/6)^4
(D) 4(1/6)^3(5/6) + (1/6)^4
(E) 6(1/6)^3(5/6) + (1/6)^4
4 times, which of the following is the probability that the outcome will be a two at
least 3 times?
(8) 2(1/6i + (1/6)4
(C) 3{1/6)3(5/6) + (1/6)4
(O) 4{1/6)3{5/6) + (1/6)4
(E) 6{1/6)3{5/6) + (1/6)4
Corrected options:
(A) (1/6)^4
(B) 2(1/6)^3 + (1/6)^4
(C) 3(1/6)^3(5/6) + (1/6)^4
(D) 4(1/6)^3(5/6) + (1/6)^4
(E) 6(1/6)^3(5/6) + (1/6)^4
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11 Sep 2011, 01:41
Kudos
Bookmarks
should there be 5 cases for this one ??
Outcomes:
2 - 2 - 2 - not a 2
2 - 2 - 2 - 2
2 -not a 2 - 2- 2
not a 2 - 2 - 2 - 2
2 - 2 - not a 2 - 2
???
Outcomes:
2 - 2 - 2 - not a 2
2 - 2 - 2 - 2
2 -not a 2 - 2- 2
not a 2 - 2 - 2 - 2
2 - 2 - not a 2 - 2
???
11 Sep 2011, 07:03
Kudos
Bookmarks
siddhans
The following is the question with correct format. Please format your questions properly. The math symbol to denote power is "^".
For one roll of a certain die, the probability of rolling a two is 1/6. If this die is rolled 4 times, which of the following is the probability that the outcome will be a two at least 3 times?
(A) (1/6)^4
(B) 2(1/6)^3 + (1/6)^4
(C) 3(1/6)^3(5/6) + (1/6)^4
(D) 4(1/6)^3(5/6) + (1/6)^4
(E) 6(1/6)^3(5/6) + (1/6)^4
*********************************************
Sol:
This is the question in which you make use of binomial distribution.
What is the probability that the outcome will be a two AT LEAST 3 times:
Outcome 2 EXACTLY 3 times
+
Outcome 2 EXACTLY 4 times
Outcome 2 EXACTLY 3 times
\(=(\frac{1}{6})^3*(1-\frac{1}{6})^1*\frac{4!}{3!}=4*(\frac{1}{6})^3(\frac{5}{6})^1\)
Outcome 2 EXACTLY 4 times
\(=(\frac{1}{6})^4*(1-\frac{1}{6})^0=(\frac{1}{6})^4\)
Outcome 2 EXACTLY 3 times = Outcome 2 EXACTLY 3 times + Outcome 2 EXACTLY 4 times
\(=4(\frac{1}{6})^3(\frac{5}{6})+(\frac{1}{6})^4\)
Ans: "D"
******************************************************
In its simplest form:
\(Answer=\frac{7}{2*6^3}=\frac{7}{432}\)
Read this:
permutation-combination-and-probabilities-14706.html#p89947
