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Re: The probability of Tom rolling a strike while bowling is 40% on any [#permalink]
Expert Reply

Solution


Given

    • The probability of Tom rolling a strike while bowling is 40% on any given frame
    • Tom rolls 4 frames in a row

To Find

    • The statements which are true.

Approach and Working Out


    • I. The probability of Tom rolling a strike on all 4 frames is greater than 3%.
      o The probability is given by,
      (\(\frac{40}{100}\))\(^4\)
      = 0.0256
      = 2.56%
      o This is false.

    • II. The probability of Tom rolling no strikes in 4 frames is less than 10%.
      o The probability is given by,
      (\(\frac{60}{100}\))\(^4\)
      = 0.1296
      = 12.96%
      o This is false.

    • III. Tom is equally likely to roll exactly 1 strike as to roll exactly 2 strikes in those 4 frames.
      o Exactly 1 strike = 4C1 × \(\frac{40}{100}\) × (\(\frac{60}{100}\))\(^3\) = 0.3456
      o Exactly 2 strike = 4C2 × (\(\frac{40}{100}\))\(^2\) × (\(\frac{60}{100}\))\(^2\) = 0.3456
      o This is true.


Correct Answer: Option C
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Re: The probability of Tom rolling a strike while bowling is 40% on any [#permalink]
Why has everyone done 4C1 and 4C2 in the statement 3 solutions.?

Is it because 1 strike is selected out 4 chances and 2 is selected out of 4 chances or some other specific reason?

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Re: The probability of Tom rolling a strike while bowling is 40% on any [#permalink]
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Nups1324 wrote:
Why has everyone done 4C1 and 4C2 in statement 3 solutions.?

Is it because 1 strike is selected out 4 chances and 2 is selected out of 4 chances or some other specific reason?

Posted from my mobile device


Hi Nups1324,

Yes, you are correct.
There are 4C1 and 4C2 ways to choose those strikes.

Regards!
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Re: The probability of Tom rolling a strike while bowling is 40% on any [#permalink]
Oh! Alright.

Thank you so much for clearing my doubt.

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Re: The probability of Tom rolling a strike while bowling is 40% on any [#permalink]
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Re: The probability of Tom rolling a strike while bowling is 40% on any [#permalink]
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