Conditional probability and independan events?

A pair of fair dice is cast.Let E denote the event that the number falling uppermost in the first die is 5 and let F denote the event that the sum of the numbers falling uppermost is 10.


a) compute P(F)


b) compute P(E and F)


c) compute P(E|F)


d) compute P(E)





Thanx

Conditional probability and independan events?
The sample space consists of 36 possible events when you throw a pair of dice.


a) P(F)=


(4,6) = 10


(5,5) = 10


(6,4) = 10


3 ways out of 36.


P(F)=3/36 = 1/12





b)(5,5) = 10


1 way; the second has to be 5 too in order for the sum to be 10.


P(E and F) = 1/36





c)P(E and F) = P(F) P(E/F)


P(E/F) = P(E and F) / P(F)


P(E/F) = (1/36) / (1/12) = 1/3





d)P(E)=


(5,1)


(5,2)


(5,3)


(5,4)


(5,5)


(5,6)


6/36 = 1/6
Reply:a) P(F)=1/12


reason: three events where sum is 10


6+4=10, 4+6=10, 5+5=10


and 36 events total s.t.


3/36=1/12





b) (1/12)(1/6) because mutually dependent events are multiplied


c) (1/6)/(1/12)


d)1/6

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