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s2 again please

An archer fires arrows at a target and for each arrow, independently of all others, the probability that it hits the bullseye is 1/8

a) Given that the archer fires 5 arrows, find the probability that fewer than 2 arrows hit the bullseye.

The archer fires 5 arrows, collects them from the target and fires all 5 again.

b) Find the probability that on both occasions fewer than 2 hit the bullseye

The archer now fires 60 arrows at the target. Using a suitable approximation find

c) the probability that fewer than 10 hit the bullseye
d) the smallest value of m such that the probability that the archer hits the bullseye with at least m arrows is greater than 0.5

Any clues would be greatly appreciated.

Thank you very much

Reply 1

Jump

18

First step identify the distribution. :smile:

Reply 2

Jackal123

OP

i've tried it using a poisson distribution but my answers dont match. Could really do with a solutiion if anyone can work it out

Reply 3

El Stevo

11

hint: its a geometric of X~Geo(0.125)

Reply 4

Jackal123

OP

Come on people.
I have to get these questions done for tomorrow and can't get past the first one.

Any help would be greatly appreciated.

Thanks

Reply 5

Jackal123

OP

can you at least show me the working for part a)

Reply 6

!Laxy!

Jackal123

An archer fires arrows at a target and for each arrow, independently of all others, the probability that it hits the bullseye is 1/8

a) Given that the archer fires 5 arrows, find the probability that fewer than 2 arrows hit the bullseye.

The archer fires 5 arrows, collects them from the target and fires all 5 again.

b) Find the probability that on both occasions fewer than 2 hit the bullseye

The archer now fires 60 arrows at the target. Using a suitable approximation find

c) the probability that fewer than 10 hit the bullseye
d) the smallest value of m such that the probability that the archer hits the bullseye with at least m arrows is greater than 0.5

Any clues would be greatly appreciated.

Thank you very much

I ain't working it out for you, but here are some clues! :smile:

a) Use binomial. n=5, p=1/8

P(X< or equal to 2)

b) answer to part (a) squared

c) Use poisson dist. To get mean do 60 x 1/8 = 7.5

So: P(X<10)

d) use the tables

Reply 7

El Stevo

11

you are prolly right !laxy! but i thought binomials were s1. thats the reason i suggested the geometric distribution. they only come in at s2...

edit: but then again, a binomial approximation to a poisson is s2 so you are probably right...

Reply 8

!Laxy!

El Stevo

you are prolly right !laxy! but i thought binomials were s1. thats the reason i suggested the geometric distribution. they only come in at s2...

depends which exam board your doing :smile:

I think there doing edexcel in which case binomials are S2 and you dont need toknow geometric :tsr:

Reply 9

Jackal123

OP

for part a) i've done 5choose2 * (1/8)^2 * (7/8)^3

But its not matching the answer.

What am I doing wrong?

Reply 10

!Laxy!

Jackal123

for part a) i've done 5choose2 * (1/8)^2 * (7/8)^3

But its not matching the answer.

What am I doing wrong?

a) says LESS than 2.

do 5choose0 (1/8)^0 (7/8)^5 + 5choose1 (1/8) (7/8)^4 :smile:

s2 again please

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