Answer:
Step-by-step explanation:
Given
--- probability of scoring
Required
Probability that his first miss is his 6th shot
Let q represent the event that he did not score.
Using complement rule:
The event that his first miss is his 6th is represented as:
p p p p p q ---- That he scoress the first 5 attempts
So, the probability is:
Prove:
Using mathemetical induction:
P(n) =
for n=1
P(n) = = 6
It is divisible by 2 and 3
Now, for n=k,
P(k) =
Assuming P(k) is divisible by 2 and 3:
Now, for n=k+1:
P(k+1) =
P(k+1) =
P(k+1) =
Since, we assumed that P(k) is divisible by 2 and 3, therefore, P(k+1) is also
divisible by 2 and 3.
Hence, by mathematical induction, P(n) = is divisible by 2 and 3 for all positive integer n.