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# The probability of Tom rolling a strike while bowling is 40% on any

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

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.

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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]
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?

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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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