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Some balls are placed in a large box, which include 1 ball marked "A",

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cat2010
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Some balls are placed in a large box, which include 1 ball marked "A", [#permalink] New post   08 Dec 2022, 03:38
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Some balls are placed in a large box, which include 1 ball marked "A", 2 balls marked "B", 3 balls marked "C", and so on up to 26 balls marked "Z".

A ball is drawn at random. Give the probability that the ball will be marked "O".

A.\(\frac{3}{65}\)

B.\(\frac{5}{117}\)

C.\(\frac{5}{234}\)

D.\(\frac{3}{130\\
}\)

E.\(\frac{3}{70}\)
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chetan2u
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Re: Some balls are placed in a large box, which include 1 ball marked "A", [#permalink] New post   08 Dec 2022, 07:02
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cat2010 wrote:
Some balls are placed in a large box, which include 1 ball marked "A", 2 balls marked "B", 3 balls marked "C", and so on up to 26 balls marked "Z".

A ball is drawn at random. Give the probability that the ball will be marked "O".

A.\(\frac{3}{65}\)

B.\(\frac{5}{117}\)

C.\(\frac{5}{234}\)

D.\(\frac{3}{130\\
}\)

E.\(\frac{3}{70}\)



Total balls = 1+2+3+…25+26 = \(\frac{26*27}{2}=13*27\)

Now if you have a number to each successive letter, 15 will stand for O or 15 balls are marked O.
Thus, there are 15 balls to pick up from.

P= \(\frac{15}{13*27}=\frac{5}{117}\)


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Re: Some balls are placed in a large box, which include 1 ball marked "A", [#permalink] New post   08 Dec 2022, 10:35
There will be 15 balls marked 'o'
Total balls = 1+2+3+4+5+...26 = 26*27/2 = 13*27
Probability = 15/13*27 = 5/117
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Some balls are placed in a large box, which include 1 ball marked "A", [#permalink] New post   08 Dec 2022, 19:01
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cat2010 wrote:
Some balls are placed in a large box, which include 1 ball marked "A", 2 balls marked "B", 3 balls marked "C", and so on up to 26 balls marked "Z".

A ball is drawn at random. Give the probability that the ball will be marked "O".

A.\(\frac{3}{65}\)

B.\(\frac{5}{117}\)

C.\(\frac{5}{234}\)

D.\(\frac{3}{130\\
}\)

E.\(\frac{3}{70}\)


We can determine the total number of balls by using the sum formula for evenly spaced sets:

Sum = avg x quantity

Sum = (1 + 26)/2 x 26

Sum = 27 x 13 = 351

Sine O is the 15th letter, there are 15 balls marked O.

Thus, the probability is 15/351 = 5/117

Answer: B
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Some balls are placed in a large box, which include 1 ball marked "A", [#permalink]
08 Dec 2022, 19:01
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