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# Students are playing a guessing game in which a player must randomly

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Math Expert
Joined: 02 Sep 2009
Posts: 47920
Students are playing a guessing game in which a player must randomly  [#permalink]

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20 Mar 2018, 23:27
00:00

Difficulty:

35% (medium)

Question Stats:

68% (01:22) correct 32% (01:48) wrong based on 57 sessions

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Students are playing a guessing game in which a player must randomly guess which of five options is correct. After each guess, a new set of five options is presented. A player’s turn continues as long as the player answers correctly. A player’s turn ends the first time the player guesses incorrectly. What is the probability a player’s turn will end after the player guesses three times?

(A) 0.008
(B) 0.032
(C) 0.128
(D) 0.488
(E) 0.512

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Joined: 02 Sep 2009
Posts: 47920
Re: Students are playing a guessing game in which a player must randomly  [#permalink]

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20 Mar 2018, 23:28
Bunuel wrote:
Students are playing a guessing game in which a player must randomly guess which of five options is correct. After each guess, a new set of five options is presented. A player’s turn continues as long as the player answers correctly. A player’s turn ends the first time the player guesses incorrectly. What is the probability a player’s turn will end after the player guesses three times?

(A) 0.008
(B) 0.032
(C) 0.128
(D) 0.488
(E) 0.512

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Re: Students are playing a guessing game in which a player must randomly  [#permalink]

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21 Mar 2018, 00:12
1
Bunuel wrote:
Students are playing a guessing game in which a player must randomly guess which of five options is correct. After each guess, a new set of five options is presented. A player’s turn continues as long as the player answers correctly. A player’s turn ends the first time the player guesses incorrectly. What is the probability a player’s turn will end after the player guesses three times?

(A) 0.008
(B) 0.032
(C) 0.128
(D) 0.488
(E) 0.512

IMO B.

The probability of a right guess = 1/5 ( 0.2 )
The probability of a wrong guess = 4/5 ( 0.8)

For the chance of a player to end after three guesses .. his or her third guess must be wrong AND his or her first two guesses must be right.

The probability of that is ->

(0.2)*(0.2)*(0.8) = 0.032
G1 G2 G3

Hence B.

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Re: Students are playing a guessing game in which a player must randomly  [#permalink]

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22 Mar 2018, 18:47
Bunuel wrote:
Students are playing a guessing game in which a player must randomly guess which of five options is correct. After each guess, a new set of five options is presented. A player’s turn continues as long as the player answers correctly. A player’s turn ends the first time the player guesses incorrectly. What is the probability a player’s turn will end after the player guesses three times?

(A) 0.008
(B) 0.032
(C) 0.128
(D) 0.488
(E) 0.512

The player's turn ended after 3 guesses, therefore he/she must guessed the first 2 right and the 3rd one wrong.
The probability to guess the question right: $$\frac{1}{5}$$
The probability to guess the question wrong: $$\frac{4}{5}$$

Since the turn will end immediately if the student answer incorrectly, the wrong answer must be in question 3 (no need to take order of arrangement into consideration)

$$P = \frac{1}{5}*\frac{1}{5}*\frac{4}{5} = \frac{4}{125}$$

$$\frac{4}{100}$$ = 0.04, therefore $$\frac{4}{125}$$ should be a little less than 0.04 => (B)
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Re: Students are playing a guessing game in which a player must randomly  [#permalink]

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26 Mar 2018, 09:49

Solution:

Given:

• The player needs to randomly guess one of five options.

• After each guess, a new set of 5 options come up.

• The game ends when the player guesses incorrectly.

Working out:

We need to find out the probability that the game ends after 3 turns.

Analysis of the guessing game:

• Total options = 5

• Correct option = 1

• Probability of getting the correct guess = $$1/5 = 0.2$$

For the game to end after 3 turns, the following is the only possibility.

• Turn1: Correct guess

• Turn 2: Correct guess

• Turn 3: Incorrect guess.

P (Game ending after 3 turns) = P (Correctly guess the first question) * P (Correctly guess the second question) * P (Incorrectly guesses the third question)

Or, P (Game ending after 3 turns) = $$1/5 * 1/5 * 4/5 = 4/ 125$$

Or, $$4/125 = 0.032$$

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Re: Students are playing a guessing game in which a player must randomly  [#permalink]

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28 Mar 2018, 10:34
Bunuel wrote:
Students are playing a guessing game in which a player must randomly guess which of five options is correct. After each guess, a new set of five options is presented. A player’s turn continues as long as the player answers correctly. A player’s turn ends the first time the player guesses incorrectly. What is the probability a player’s turn will end after the player guesses three times?

(A) 0.008
(B) 0.032
(C) 0.128
(D) 0.488
(E) 0.512

The probability that a turn ends after guessing 3 times is 1/5 x 1/5 x 4/5 = 4/125 = 0.032.

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Re: Students are playing a guessing game in which a player must randomly &nbs [#permalink] 28 Mar 2018, 10:34
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