probability problem!!!need help?

Question

the probability that a amarksman will hit a target is 4/5. He fires 10 shots.
if he hits the target exactly 7 times, calculate the probability that the 3misses are with successive shots.

Answer 1

the probability that he will hit a target when he shoots is 1 out of 5. when you want to know the probability of two events occuring at the same time, you multiply them. the probability that he will miss three times in a row is 1 out of 125 (1/5*1/5*1/5).

the fact that he hit the target the first 7 times doesn't matter. he has a 4 out of 5 chance of hitting a target every time he shoots. the gun doesn't have a memory of past events.

Answer 2

Since this is a conditional probability we have 7 hits out of 10 shots as a given.

Calculate the probability that the three misses are consecutive.

The number of arrangments of the shots is:

C(10,7) = 10!/[(7!)(3!)] = 10*9*8/3! = 120

Of these, three consecutive misses can be in positions

123
234
...
89(10)

There are 8 possibilities.

So the probability of 3 consecutive misses is:

8/120 = 1/15