Afair die is rolled repeatedly. use precise notation of probabilities of events and random variables for the solutions to the questions below.

(a) write down a precise sum expression for the probability that the first five rolls give a 3 at most two times.

(b) calculate the probability that the first 3 does not appear before the fifth roll.

(c) calculate the probability that the first 3 appears before the twentieth roll but not before the fifth roll

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step-by-step explanation:

hope it you

step-by-step explanation:

sin(7pi/6 - pi/3)  

= sin(7pi/6 - 2pi/6)  

= sin(5pi/6)  

= sin(pi - pi/6)  

= sin(pi/6)  

= 1/2  

sin 7pi/6 - sin pi/3  

= sin (pi + pi/6) - sin pi/3  

= -sin pi/6 - sin pi/3  

= -1/2 - sqrt(3)/2  

= -(1+sqrt(3))2

check above link.

graphically?   well, you graph them both, the solutions is where they both intersect each other, since there are two solutions, meaning they will meet twice, or namely the linear will run into the quadratic curve twice, and where they meet, those x,y coordinates are the solutions to the system.

think the answer would beb