Probability of result

Question

Morning,

A inbound contact centre says they will answer calls within 3 mins 70% of the time, if I ring the call centre 5 times over a week what is the probability I get my calls answered in under 3 mins more than 3 times?

P(a) = 0.7 P(b) = 0.3 P(X >3) Could someone walk me through how to do this?

Answer 1

Hint:

You can try to find by using binomial distribution which you want to find P(X=4)+P(X=5)

You have to set the number of trials n=5 and p=0.7.

$X\sim Bin (n,p)$

$P(X=4)= \binom{5}{4}0.7^4(1-0.7)^1$

$P(X=5)= \binom{5}{5}0.7^5(1-0.7)^0$

Hope this helps

Answer 2

Suppose you have a spinner and 70% of the spinner is colored red and the other 30% is colored blue. Let's say you spin the spinner and you "win" when it is red.

0.) What is the probability of winning one spin?

Now suppose I spin the spinner 5 times in a row and each time it comes up red, I win.

1.) Are each of the 5 spins dependent or independent events?

2.) Can you calculate the probability of winning 5 times in a row?

How is this game like making calls and getting your call answered in 3 minutes or less.

Good luck!