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# Nora will enter a ticket lottery every day until she wins the lottery,

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Senior SC Moderator
Joined: 14 Nov 2016
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Nora will enter a ticket lottery every day until she wins the lottery, [#permalink]

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10 Feb 2017, 00:23
00:00

Difficulty:

35% (medium)

Question Stats:

63% (00:35) correct 37% (01:06) wrong based on 49 sessions

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Nora will enter a ticket lottery every day until she wins the lottery, after which she will no longer enter. If the probability that she wins the ticket lottery is $$0.1$$ on each of the first three days, what is the probability that she wins on the third day?

(A) $$0.001$$
(B) $$0.009$$
(C) $$0.081$$
(D) $$0.729$$
(E) $$0.900$$
[Reveal] Spoiler: OA

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Re: Nora will enter a ticket lottery every day until she wins the lottery, [#permalink]

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10 Feb 2017, 07:22
ziyuenlau wrote:
Nora will enter a ticket lottery every day until she wins the lottery, after which she will no longer enter. If the probability that she wins the ticket lottery is $$0.1$$ on each of the first three days, what is the probability that she wins on the third day?

(A) $$0.001$$
(B) $$0.009$$
(C) $$0.081$$
(D) $$0.729$$
(E) $$0.900$$

I don't see a correct answer. If the probability she wins on any given day of the first three days is 0.1 the "the probability she wins on the third day" would still be 0.1
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Re: Nora will enter a ticket lottery every day until she wins the lottery, [#permalink]

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10 Feb 2017, 08:22
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IdiomSavant wrote:
ziyuenlau wrote:
Nora will enter a ticket lottery every day until she wins the lottery, after which she will no longer enter. If the probability that she wins the ticket lottery is $$0.1$$ on each of the first three days, what is the probability that she wins on the third day?

(A) $$0.001$$
(B) $$0.009$$
(C) $$0.081$$
(D) $$0.729$$
(E) $$0.900$$

I don't see a correct answer. If the probability she wins on any given day of the first three days is 0.1 the "the probability she wins on the third day" would still be 0.1

Look carefully again at the highlighted part....

Nora entered Ticket Lottery coz she didn't win it on the first 2 days..

Probability of not winning lottery on the first 2 days is 0.9*0.9 = 0.081

Hence, correct answer must be (C) 0.081

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Nora will enter a ticket lottery every day until she wins the lottery, [#permalink]

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10 Feb 2017, 08:25
Abhishek, good reply; beat me to it by 2 minutes! EDIT: But it does need to say 0.9 * 0.9 * 0.1. Shame on me for not reading closely enough.

Fun twist: If you know that Nora did, in fact, win on one of the first three days, what's the probability she won on day 3?

Last edited by AnthonyRitz on 10 Feb 2017, 09:01, edited 1 time in total.
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Joined: 14 Sep 2016
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Nora will enter a ticket lottery every day until she wins the lottery, [#permalink]

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10 Feb 2017, 08:57
Abhishek009 wrote:
IdiomSavant wrote:
ziyuenlau wrote:
Nora will enter a ticket lottery every day until she wins the lottery, after which she will no longer enter. If the probability that she wins the ticket lottery is $$0.1$$ on each of the first three days, what is the probability that she wins on the third day?

(A) $$0.001$$
(B) $$0.009$$
(C) $$0.081$$
(D) $$0.729$$
(E) $$0.900$$

I don't see a correct answer. If the probability she wins on any given day of the first three days is 0.1 the "the probability she wins on the third day" would still be 0.1

Look carefully again at the highlighted part....

Nora entered Ticket Lottery coz she didn't win it on the first 2 days..

Probability of not winning lottery on the first 2 days is 0.9*0.9 = 0.081

Hence, correct answer must be (C) 0.081

You're missing a step though right?

Probability of not winning lottery on the first 2 days is 0.9*0.9=0.81 not 0.081 yet.

The probability of winning on the third day is 0.81*0.1 = 0.081 (Probability of making it to the third day x probability of winning on day 3).
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Re: Nora will enter a ticket lottery every day until she wins the lottery, [#permalink]

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15 Feb 2017, 09:50
ziyuenlau wrote:
Nora will enter a ticket lottery every day until she wins the lottery, after which she will no longer enter. If the probability that she wins the ticket lottery is $$0.1$$ on each of the first three days, what is the probability that she wins on the third day?

(A) $$0.001$$
(B) $$0.009$$
(C) $$0.081$$
(D) $$0.729$$
(E) $$0.900$$

We are given that Nora’s probability of winning the lottery on each of the first 3 days is 0.1; thus, the probability of her not winning on any day is 1 - 0.1 = 0.9. We must determine the probability of her winning on day 3, which means she does not win on day 1 or on day 2.

P(winning on day 3) = 0.9 x 0.9 x 0.1 = 0.081.

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Re: Nora will enter a ticket lottery every day until she wins the lottery, [#permalink]

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15 Feb 2017, 19:04
Since this question gives you the probability of winning (1/10), it is implied that the probability of losing is (9/10)

The question basically asks: (9/10)*(9/10)*(1/10) = ?
-- 81/1,000 --> .081
Re: Nora will enter a ticket lottery every day until she wins the lottery,   [#permalink] 15 Feb 2017, 19:04
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