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555-605 Level|   Probability|      
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Bunuel
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There are 100 marbles in a jar. Forty of the marbles are black and 60 22 Apr 2018, 22:13
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E
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Difficulty:

35% (medium)

Question Stats:

72% (01:59) correct 28% (02:23) wrong based on 210 sessions

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There are 100 marbles in a jar. Forty of the marbles are black and 60 are white. What is the probability of getting at least one black marble in three consecutive picks, with replacement of the marble each time?

A. 0.216
B. 0.316
C. 0.500
D. 0.684
E. 0.784
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E
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There are 100 marbles in a jar. Forty of the marbles are black and 60 22 Apr 2018, 22:26
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Bunuel
There are 100 marbles in a jar. Forty of the marbles are black and 60 are white. What is the probability of getting at least one black marble in three consecutive picks, with replacement of the marble each time?

A. 0.216
B. 0.316
C. 0.500
D. 0.684
E. 0.784

P(atleast 1 Black in three cons picks)= 1 - P( All white picks in cons 3 picks)

= 1- (\(\frac{60}{100})^3\) = 0.784 ans E

Since it is replacement so we have same P hence cube
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There are 100 marbles in a jar. Forty of the marbles are black and 60 09 May 2018, 06:41
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Probability of at least one black=1- (all white)

=1-(60*60*60/(100*100*100))
=1-0.216
=0.784

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There are 100 marbles in a jar. Forty of the marbles are black and 60 06 Mar 2020, 08:41
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Probability of getting AT LEAST 1 Black marble = 1-(Probability of getting white marble)

Hence,
=1-(60/100)(60/100)(60/100)
=1-(0.6)^3
=1-0.216
=0.784

Note:Use cube of 6 to get the answer quickly.

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There are 100 marbles in a jar. Forty of the marbles are black and 60 09 Mar 2020, 04:42
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Bunuel
There are 100 marbles in a jar. Forty of the marbles are black and 60 are white. What is the probability of getting at least one black marble in three consecutive picks, with replacement of the marble each time?

A. 0.216
B. 0.316
C. 0.500
D. 0.684
E. 0.784

Solution:

We can use the equation:

P(at least one black marble) = 1 - P(no black marbles)

P(at least one black marble) = 1 - P(all white marbles)

P(at least one black marble) = 1 - (3/5 x 3/5 x 3/5)

P(at least one black marble) = 1 - 27/125 = 1 - 216/1000 = 1 - 0.216 = 0.784

Alternate Solution:

The long way is to consider that any of the following cases will satisfy the requirement:

Case 1. One black and two white: BWW, WBW, WWB, and each outcome has a probability of 2/5 x 3/5 x 3/5 = 18/125. Because there are 3 different outcomes, multiply by 3 to get 54/125.

Case 2. Two black and one white: WBB, BWB, BBW , and each outcome has a probability of 3/5 x 2/5 x 2/5 = 12/125. Because there are 3 different outcomes, multiply by 3 to get 36/125

Case 3. Three black: BBB, with probability 2/5 x 2/5 x 2/5 = 8/125.

Thus, the probability of getting at least one black marble is the sum: 54/125 + 36/125 + 8/125 = 98/125.= 0.784.

Answer: E
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