Thread: probability ("at least one", "at most one") help

Two professors: Prof. Strange and Prof. Boring.

100 published papers. 45% published by Strange. 35% published by Boring. 10% of the papers involve both professors.

Let A denote publication by Strange
Let B denote publication by Boring

P(A)= .45
P(B)= .35
P(A intersect B) = .1

How many of the published papers were authored by:
a.) neither Strange nor Boring?

addition rule: P(A union B)= P(A)+P(B)-P(A intersect B), resulting in
P(A union B) = .7, or 70 papers involved either professor, take the compliment of P(A union B),meaning:
30 papers have nothing to do with Strange nor Boring.

Now, where I get confused:

b.) How many published papers were authored by at most one of these two professors?

How would I go about answering this?

Originally Posted by rewtuser

Two professors: Prof. Strange and Prof. Boring.

100 published papers. 45% published by Strange. 35% published by Boring. 10% of the papers involve both professors.

Let A denote publication by Strange
Let B denote publication by Boring

P(A)= .45
P(B)= .35
P(A intersect B) = .1

How many of the published papers were authored by:
a.) neither Strange nor Boring?

addition rule: P(A union B)= P(A)+P(B)-P(A intersect B), resulting in
P(A union B) = .7, or 70 papers involved either professor, take the compliment of P(A union B),meaning:
30 papers have nothing to do with Strange nor Boring.

Now, where I get confused:

b.) How many published papers were authored by at most one of these two professors?

How would I go about answering this?

P(A)+P(B) counts the papers with A as author only and the papers qith B as author only and 2 times the number of papers with both, so

P((A union B)\(A intersection B))=P(A)+P(b)-2P(A intersection B)=0.6

RonL