we have four aunts going to a party: Albertine (0.3) Karoline (0.5) Makronelle (0.8) Petronelle (0.9)
a) find the probability that exactly two of the four aunts come to the party.
b) find the probability that noone comes to the party.
c) what is the probability that at most 2 coem to the party.
d) find the conditional probability that patronelle comes given taht exactly two aunts comes.
anyone know how to go go about these questions? on b) I think its just 0.7*0.5*0.2*0.1=7/1000? not sure about the other questions tho? any tips/solutions?
Best Answer
Part (a):
Let A be the event Albertine comes to the party, K be the event Karoline comes to the party, etc. The cases where exactly two aunts come are: AK AM AP KM KP MP
$P(AK) = 0.3 \times 0.5 \times 0.2 \times 0.1$ (Albertine and Karoline come but Markronlle and Petronelle don't).
Find the probabilities for the other cases and add them up.
Part (b):
What you have is correct.
Part (c):
Add the probabilities that 0, 1, and 2 come. You have the probabilities that 0 and 2 come from the previous parts. So add the four cases where only one comes. For example, if only Albertine comes the probability is $0.3 \times 0.5 \times 0.2 \times 0.1$
Part (d):
The probabilities are independent so the probability that Petronelle comes is still $0.9$.