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# On every game, there are only two cases: the player wins or loses

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Senior CR Moderator
Status: Long way to go!
Joined: 10 Oct 2016
Posts: 1389
Location: Viet Nam
On every game, there are only two cases: the player wins or loses [#permalink]

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11 Dec 2016, 05:50
1
1
00:00

Difficulty:

95% (hard)

Question Stats:

40% (01:53) correct 60% (01:41) wrong based on 107 sessions

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On every game, there are only two cases: the player wins or loses. The probability that Michael wins on each game is 0.4. How many games does Michael have to play at least so that the probability that Michael wins on at least one game is greater than 0.95?

A. 4
B. 5
C. 6
D. 7
E. 8

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Senior Manager
Joined: 13 Oct 2016
Posts: 367
GPA: 3.98
Re: On every game, there are only two cases: the player wins or loses [#permalink]

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11 Dec 2016, 09:22
2
Hi

P(winning at least one game)>0,95 is the same as P(loosing all)<0,05

$$0,6^n < 0,05$$

$$n=5 ----> 0,0777...$$

$$n=6 ----> 0,04665...$$

Senior Manager
Joined: 13 Oct 2016
Posts: 367
GPA: 3.98
Re: On every game, there are only two cases: the player wins or loses [#permalink]

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11 Dec 2016, 23:07
Another way to calculate:

$$0.6^n < 0.05$$

$$ln (6^n) < ln(0.05)$$

$$n*ln(0.6) < ln(0.05)$$

$$n*(-0.5108) < -2.9957$$

$$n > 5.864..$$

Min integer value of $$n$$ is $$6$$.

Although it's hard to be done without calculator
Intern
Joined: 12 Dec 2016
Posts: 1
Re: On every game, there are only two cases: the player wins or loses [#permalink]

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13 Dec 2016, 13:27
Probability of wining AT LEAST one game is 1 - probability of wining no games:

1 - P(0) = P(>=1)

If we want the probability of wining at least 1 games to be at least 95% (>=0.95); then probability of wining no games has to be less than or equal to 5% (<=.05).

Probability of losing a game [P(0)] is (6/10)^ n, where n is the number of games played.

We start with option c to know if we should go up or down if c is false.

(6/10)^6 = 45,792/1000000= 0.045792 chance that you lose 6 games in a row

The probability of winning at least 1 game is 1 - P(0)
1 - 0.045792 > .95

Retired Moderator
Status: The best is yet to come.....
Joined: 10 Mar 2013
Posts: 533
Re: On every game, there are only two cases: the player wins or loses [#permalink]

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18 Aug 2017, 07:16
A similar tough and tricky question is here

https://gmatclub.com/forum/tough-and-tr ... 85179.html
_________________

Hasan Mahmud

Re: On every game, there are only two cases: the player wins or loses   [#permalink] 18 Aug 2017, 07:16
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