i'm currently trying to understand conditional probabilities but there is one small thing that i haven't been able to understand.
how do you calculate a plain intersections?
Say you throw two dices, a red one first and then a blue one
event a: total numbers of eyes is atleast 7
event b maximum of the two single throws is at most five
; P(a) 21/36\, p(b) 25/36
What is intersection of a and b? (P(A ∩ B))
i understand the intuition behind it but i want a mathematical way to calculate this.
Thank you!!

Question

i'm currently trying to understand conditional probabilities but there is one small thing that i haven't been able to understand. 
how do you calculate a plain intersections?
Say you throw two dices, a red one first and then a blue one
event a: total numbers of eyes is atleast 7
event b maximum of the two single throws is at most five
; P(a) 21/36\, p(b) 25/36
What is intersection of a and b? (P(A ∩ B))
i understand the intuition behind it but i want a mathematical way to calculate this.
Thank you!!

anonymous · Answer

P(a) 21/36\, p(b) 25/36**** miss typed that!!!

turingtest · Answer

my probability skills are a but rusty, the only general formula for the intersection that i know of is$$P(A\cap B)=P(A)+P(B)-P(A\cup B)$$but the intuition is more important, and is usually more valuable in finding ways to solve such problems

turingtest · Answer

i would usually make a tree in such problems as these

anonymous · Answer

thank you man!

turingtest · Answer

welcome :)