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# The probability of Loki getting a question correct on a certain exam

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The probability of Loki getting a question correct on a certain exam  [#permalink]

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Updated on: 06 Feb 2019, 06:02
00:00

Difficulty:

55% (hard)

Question Stats:

60% (02:16) correct 40% (02:19) wrong based on 68 sessions

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The probability of Loki getting a question correct on a certain exam is 75 percent. If Loki answers three test questions in a row, what is the probability that he gets at least two of the questions wrong?

A) $$\frac{5}{64}$$

B) $$\frac{5}{32}$$

C) $$\frac{3}{16}$$

D) $$\frac{7}{32}$$

E) $$\frac{5}{16}$$

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Originally posted by Abhi077 on 06 Feb 2019, 05:59.
Last edited by Bunuel on 06 Feb 2019, 06:02, edited 1 time in total.
Renamed the topic and edited the question.
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Re: The probability of Loki getting a question correct on a certain exam  [#permalink]

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06 Feb 2019, 06:25
2
Probability(Right) = 3/4
Probability(Wrong) = 1/4

At least two wrong = RRW+RWR+WRR+RRR = 9/64+1/64 = 10/64 = 5/32

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Re: The probability of Loki getting a question correct on a certain exam  [#permalink]

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06 Feb 2019, 10:05
Abhi077 wrote:
The probability of Loki getting a question correct on a certain exam is 75 percent. If Loki answers three test questions in a row, what is the probability that he gets at least two of the questions wrong?

A) $$\frac{5}{64}$$

B) $$\frac{5}{32}$$

C) $$\frac{3}{16}$$

D) $$\frac{7}{32}$$

E) $$\frac{5}{16}$$

Correct = 75% = 3/4
Wrong = 1/4

Now at least 2 wrong out of 3

3!/2! (1/4)*(1/4)*(3/4) + 1/64

10/64

5/32

B
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Re: The probability of Loki getting a question correct on a certain exam  [#permalink]

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11 Feb 2019, 06:22
KanishkM wrote:
Abhi077 wrote:
The probability of Loki getting a question correct on a certain exam is 75 percent. If Loki answers three test questions in a row, what is the probability that he gets at least two of the questions wrong?

A) $$\frac{5}{64}$$

B) $$\frac{5}{32}$$

C) $$\frac{3}{16}$$

D) $$\frac{7}{32}$$

E) $$\frac{5}{16}$$

Correct = 75% = 3/4
Wrong = 1/4

Now at least 2 wrong out of 3

3!/2! (1/4)*(1/4)*(3/4) + 1/64

10/64

5/32

B

can you please tell me where you got 1/64 from? I was following till 1/64 showed up haha
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Re: The probability of Loki getting a question correct on a certain exam  [#permalink]

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11 Feb 2019, 06:29
eddie9233 wrote:
KanishkM wrote:
Abhi077 wrote:
The probability of Loki getting a question correct on a certain exam is 75 percent. If Loki answers three test questions in a row, what is the probability that he gets at least two of the questions wrong?

Correct = 75% = 3/4
Wrong = 1/4

Now at least 2 wrong out of 3

3!/2! (1/4)*(1/4)*(3/4) + 1/64

10/64

can you please tell me where you got 1/64 from? I was following till 1/64 showed up haha

Sure eddie9233

So the question is asking for at least 2 wrong,

1/64 is the case when all 3 question are wrong, 1/4 * 1/4 * 1/4
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Re: The probability of Loki getting a question correct on a certain exam  [#permalink]

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12 Feb 2019, 19:56
Abhi077 wrote:
The probability of Loki getting a question correct on a certain exam is 75 percent. If Loki answers three test questions in a row, what is the probability that he gets at least two of the questions wrong?

A) $$\frac{5}{64}$$

B) $$\frac{5}{32}$$

C) $$\frac{3}{16}$$

D) $$\frac{7}{32}$$

E) $$\frac{5}{16}$$

We need to determine the probability that Loki answers at least two questions wrong, so:

P(C-W-W) or P(W-W-W)

P(C-W-W) = 3/4 x 1/4 x 1/4 = 3/64

Since C-W-W can be arranged in 3!/2! = 3 ways, the probability is 3 x 3/64 = 9/64.

P(W-W-W) = (1/4)^3 = 1/64

Thus, the probability of answering at least two questions wrong is 9/64 + 1/64 = 10/64 = 5/32.

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The probability of Loki getting a question correct on a certain exam  [#permalink]

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13 Sep 2019, 03:43
Abhi077 wrote:
The probability of Loki getting a question correct on a certain exam is 75 percent. If Loki answers three test questions in a row, what is the probability that he gets at least two of the questions wrong?

A) $$\frac{5}{64}$$
B) $$\frac{5}{32}$$
C) $$\frac{3}{16}$$
D) $$\frac{7}{32}$$
E) $$\frac{5}{16}$$

CASES
$$WWR: (1/4)^2(3/4)•(3!/2!)=3/64•3=9/64$$ ($$(3!/2!)$$ is how many ways we can arrange WWR);
$$WWW: (1/4)^3=1/64$$;
$$P(WWR+WWW)=10/64=5/32$$

The probability of Loki getting a question correct on a certain exam   [#permalink] 13 Sep 2019, 03:43