Two fair dice, one blue and one red, are tossed, and the upface on each die is r

Question

Two fair dice, one blue and one red, are tossed, and the upface on each die is recorded. Define the following events: E:Image for Two fair dice, one blue and one red, are tossed, and the upface on each die is recorded. Define the following A 1 on the blue die Image for Two fair dice, one blue and one red, are tossed, and the upface on each die is recorded. Define the following F:Image for Two fair dice, one blue and one red, are tossed, and the upface on each die is recorded. Define the following The numbers are equal Image for Two fair dice, one blue and one red, are tossed, and the upface on each die is recorded. Define the following Find the following probabilities: (a) P(E)=1/2 (b) P(F)= (c) P(EImage for Two fair dice, one blue and one red, are tossed, and the upface on each die is recorded. Define the following F)= (d) P(EImage for Two fair dice, one blue and one red, are tossed, and the upface on each die is recorded. Define the following F)= (e) P(FImage for Two fair dice, one blue and one red, are tossed, and the upface on each die is recorded. Define the following E)= Are events E and F independent? A. no B. yes

Explanation / Answer

(a)  P(E)= The probability of getting a 1 on the blue die = 1/6
(b)  P(F)= The probability that the numbers on the two die are equal=6/36=1/6
(c)  P(E and F)= Proababilit of getting a 1 on blue and the numbers on the two die are equal=1/36
(d)  P(E|F)= P(E and F)/P(F)=(1/36)/(1/6)=1/6
(e)  P(F|E)= P(F and E)/P(E)=(1/36)/(1/6)=1/6
The events are independent because the outcome of the two dice do not affect each other.

Yes, the events are independent.

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