Question

Sarah went to the Carnival and decides to go bowling. She bowls by trying to knock the pins down. If the probability that Sarah misses her target is 0.40 and the result of her successful hits are independent, what is the probability that her turn lasts 7 rounds?

What is the type of distribution use for this problem?

What are the pertinent parameters?

Is it discrete or continuous?

Answer 1

Here sara's P( missing target/failure ) = 0.40

so P( hitting target / success )= 1-0.40=0.60

her turn is lasts at 7 round means at 7th round she get success

means there are 6 failures before first success with p(success) = p = 0.60

So here X = number of failure before first success which follows geometric distribution with parameter (p)

So 1. the distribution is geometric distribution.

2. parameter p = P( success) = 0.60

3. it is discrete distribution

P(X=x) = p*(1-p)^x

here x = 6

P( lasts 7 th round ) = P(X=6) 0.60*0.40^6 =0.60*0.004096 = 0.002458

So probability of her turns lasts 7th round = 0.002458