Probability question

1. Apr 11, 2013

Tomp

Question
An expert sharpshooter misses a target 10 percent of the time.

I have a question
"What is the probability that the fi rst miss comes after the 3rd shot?"

Is this as simple as 0.9^3 * 0.1?

2. Apr 12, 2013

Bacle2

Look at the sample space :

{ HHHM, HHHHM,.....}

Last edited: Apr 12, 2013
3. Apr 12, 2013

Simon Bridge

Yep, the key word is "after".

4. Apr 12, 2013

HallsofIvy

Staff Emeritus
The question is "does 'after'" mean "immediately after" or would five hits and then a miss be "the first miss is after the first three shots".

If you mean the first, then, yes, (.9)^3(.01) is correct.

If the second, then you need to expand that to larger numbers of initial hits:
(.9)^3(.01)+ (.9)^4(.01)+ (.9)^5(.01)+...

You might recognize that as part of a geometric sequence and so find a simple formula for sum.

5. Apr 12, 2013

ssd

Not 0.01 but 0.1 in all cases.:)

It is interesting to check, if we consider the 'after case' (not immediately after) then the asked event is nothing but "3 hits in first 3 shots" (whatever happens later does not matter). Therefore the answer will be (0.9)^3.

Last edited: Apr 12, 2013