Mathematics, 05.08.2020 18:01 issaaamiaaa15

An urn contains 9 red marbles, 6 white marbles, and 8 blue marbles marbles. A child randomly selects three (without replacement) from the urn. Find the probability all three marbles are the same color

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Using the probability concept, it is found that there is a 0.0903 = 9.03% probability all three marbles are the same color.

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A probability is the number of desired outcomes divided by the number of total outcomes.The order in which the marbles are chosen is not important, and they are also chosen without replacement, which means that the combination formula is used to find the number of outcomes.

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Combination formula:

$C_{n,x}$ is the number of different combinations of x objects from a set of n elements, given by the following formula.

$C_{n,x} = \frac{n!}{x!(n-x)!}$

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The desired outcomes can be:

3 from a set of 9(all red).3 from a set of 6(all white).3 from a set of 8(all blue).

Thus:

$D = C_{9,3} + C_{6,3} + C_{8,3} = \frac{9!}{3!6!} + \frac{6!}{3!3!} + \frac{8!}{3!5!} = 160$

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The total outcomes are 3 from a set of 9 + 6 + 8 = 23. Thus:

$T = C_{23,3} = \frac{23!}{3!20!} = 1771$

The probability is:

$p = \frac{D}{T} = \frac{160}{1771} = 0.0903$

0.0903 = 9.03% probability all three marbles are the same color.

A similar problem is given at link

Answer from: chem1014

P(identical colours) = 160/1771 (0.0903 to four decimals)

Step-by-step explanation:

Given 9R, 6W and 8B marbles (total = 9+6+8 = 23)

Choose three without replacement.

Need probability three identical colours.

Use the multiplication rule.

P(RRR) = 9/23 * 8*22 * 7*21 = 12 / 253

P(WWW) = 6/23 * 5/22 * 4/21 = 20/1771

P(BBB) = 8/23 * 7/22 * 6/21 = 8/153

Probability of getting identical colours

= P(RRR)+P(WWW)+P(BBB)

= 160/1771 (0.0903 to four decimals)

Answer from: Quest

the one that has a slope of 1/2 and is positive.

step-by-step explanation: 2 buckets 1 trip ; 4 buckets 2 trips and so on.

Answer from: Quest

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