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655-705 Level|   Probability|      
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Bunuel
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The integers 1 through 5 are written on each of five cards. The cards 23 Sep 2021, 02:30
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B
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65% (hard)

Question Stats:

61% (02:44) correct 39% (02:32) wrong based on 137 sessions

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The integers 1 through 5 are written on each of five cards. The cards are shuffled and one card is drawn at random. That card is then replaced, the cards are shuffled again and another card is drawn at random. This procedure is repeated one more time (for a total of three times). What is the probability that the sum of the numbers on the three cards drawn was between 13 and 15, inclusive?

A. 1/25
B. 2/25
C. 3/25
D. 4/25
E. 1/5
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B
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Chasingthesun
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The integers 1 through 5 are written on each of five cards. The cards 23 Sep 2021, 04:12
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total no of outcomes = 25
favourable outcomes = 4 i.e (5,5,5 / 5,5,4 / 5,4,4 / 5,5,3)

IMO ans D
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RanonBanerjee
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The integers 1 through 5 are written on each of five cards. The cards 25 Sep 2021, 00:26
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Ans: 2/25 (B).

Total number of outcomes: 5^3=125

13 if outcomes are (5,4,4 and 5,5,3) which can be arranged 6 ways (544, 454, 445 & 553, 355,535) respectively.

14 if outcomes are 554 with 3 arrangements (554,545,455)

15 only if we have 555. I.e, only 1 arrangement is possible.


Probability= (6+3+1)/125 =10/125= 2/25

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The integers 1 through 5 are written on each of five cards. The cards 25 Sep 2021, 08:43
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Chasingthesun
total no of outcomes = 25
favourable outcomes = 4 i.e (5,5,5 / 5,5,4 / 5,4,4 / 5,5,3)

IMO ans D
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I am sorry,I was probably sleeping when I wrote this
Horrible mistake :cry: :cry:

Total no of outcomes : 5^3
Fav outcomes : 10

Total possibilities : 10/5^3 = 2/25 ans B

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The integers 1 through 5 are written on each of five cards. The cards 25 Sep 2021, 21:46
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Correct Option B

Replacement : Multiplication with same possibility
Not Replacement : Factorization with same possibility.

Here possibility : 3, with replacement : 5*5*5 = 125

Condition 2: Sum must be in range {13 to 15} from numbers 1,2,3,4,5 named on the cards.
Possibility 1 : 555
Possibility 3 : 554, 545, 455
Possibility 6 : 543, 534, 435, 453, 345, 354
Total : 10
Probability sum {13 to 15} = 10/125 = 2/25 is option B

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The integers 1 through 5 are written on each of five cards. The cards 28 Sep 2021, 03:02
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Chasingthesun
total no of outcomes = 25
favourable outcomes = 4 i.e (5,5,5 / 5,5,4 / 5,4,4 / 5,5,3)

IMO ans D
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hi,
shouldn't the total outcomes be 125
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The integers 1 through 5 are written on each of five cards. The cards 30 Sep 2021, 10:31
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amaanshariyarr
Chasingthesun
total no of outcomes = 25
favourable outcomes = 4 i.e (5,5,5 / 5,5,4 / 5,4,4 / 5,5,3)

IMO ans D
hi,
shouldn't the total outcomes be 125
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that's right. I don't know what I was thinking when I wrote 25 :( :dazed
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The integers 1 through 5 are written on each of five cards. The cards 03 Nov 2021, 07:55
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Bunuel
The integers 1 through 5 are written on each of five cards. The cards are shuffled and one card is drawn at random. That card is then replaced, the cards are shuffled again and another card is drawn at random. This procedure is repeated one more time (for a total of three times). What is the probability that the sum of the numbers on the three cards drawn was between 13 and 15, inclusive?

A. 1/25
B. 2/25
C. 3/25
D. 4/25
E. 1/5
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This question is a part of Are You Up For the Challenge: 700 Level Questions collection.
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The integers 1 through 5 are written on each of five cards. The cards 16 May 2025, 08:29
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