Binomial distribution problem: For every 20 balls faced,....

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A cricketer knows that for every 20 balls faced she hits a 4. If she faces two overs (12 balls). Find the probability that she hits

a) two 4s
b) half the balls for 4
c) every ball for 4

For those who don't know cricket, 1 over = 6 balls bowled...

thank you in advance
 
Re: Binomial distribution problem

americo74 said:
A cricketer knows that for every 20 balls faced she hits a 4. If she faces two overs (12 balls). Find the probability that she hits

a) two 4s

I hope I understand correctly, as I am unfamiliar with cricket. Use the binomial distribution.

\(\displaystyle \begin{pmatrix}12\\2\end{pamtrix}(\frac{1}{20})^{2}(\frac{19}{20})^{10}\approx{9.8%}\)

b) half the balls for 4
c) every ball for 4

For those who don't know cricket, 1 over = 6 balls bowled...

thank you in advance
 
It's a little wierd to know about 20 balls, if balls always come in 6s.
 
Thank you

I found your bottom statement very confusing, can you please explain it?
 
Just a comment on problem design. I feel problem statements should make sense. I know nothing of cricket. Perhaps that is what I reveal by my comment.

Does it make sense to know about a rate per 20 balls? Is that how hitters are compared in cricket? To me, it seems a little odd, since an "over" is 6 balls and 20 is not a multiple of 6. Is an "over" really always 6 balls, or is it as many as 6 balls, often being cut short by a "hit"?

In this case, there is enough information to solve the problem, whether it makes sense or not. Does the question make sense? That's all I'm wondering.

In American baseball, a batting average is calculated, effectively:

hits / 1000 at-bats

I do not know why 1000 was selected, except that it is normally large enough to differentiate most hitters from most other hitters. 20 seems like an awfully small number, as it provides only 20 different hitter ratings. Maybe that's good, fine, or simply traditional.

I am rambling a bit quite on purpose. I want to emphasize thinking while reading and solving problems. Leave no stone unturned! It's never only about the arithmetic.
 
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