Question

) Quarantine restrictions lift. You’re headed straight to the nearest Irish pub. However, due to the duration of quarantine, you’re socially out of practice, and all you can think about while you’re there is stats! You take a look around and notice that the probability of seeing someone with a beer in their hand is 0.64. The probability of seeing someone drunk is 0.83. The probability of seeing someone drunk, and holding a beer is only 0.60. Finish the following calculations. SHOW WORK!

a) Is the probability of seeing someone drunk and seeing someone with beer independent? Show your work.
b) You decide to strike a conversation with someone who isn’t holding a beer. What is the probability they are drunk?
c) There are three musicians on stage playing Rattlin’ Bog. What is the probability that at least one of them is not drunk?
d) You spot one of your friends! What is the probability she is neither drunk, nor holding a beer?

Answer 1

probability of seeing someone with a beer in their hand is

probability of seeing someone drunk is

probability of seeing someone drunk, and holding a beer is only

we want

a) Is the probability of seeing someone drunk and seeing someone with beer independent?

for independence we need to show that

for the observations,

and since

we conclude that both variables are not independent. Hence the probability of seeing someone drunk and seeing someone with beer is dependent.

b) You decide to strike a conversation with someone who isn’t holding a beer. What is the probability they are drunk?

probability that someone isn't holding a beer is given by

We want the probability that they are drunk

which is given by the formula:-

hence

d) You spot one of your friends! What is the probability she is neither drunk, nor holding a beer?

we want probability she is neither drunk, nor holding a beer whcih is given by the formula

hence probability she is neither drunk, nor holding a beer is 0.40