Roll a fair die 6 times and read the number on the upper face. (a) what’s the probability of observing all possible numbers 1 to 6? (b) what’s the probability of observing three 6-s and three 1-s? (c) what’s the probability of observing two 1-s, two 3-s and two 5-s? (d) what’s the probability of observing six even numbers?

a) every number is a 1/6 chance so 6×1/6 = 1/36

b) also 1/36 because the chance doesnt change. if you throw 6 twice, the chance for a third time is still 1/6.

c) 1/36

d) 2, 4 and 6 are even so now the chance is 3/6 = 1/2 and that times 6

5=812a+9+3

step 1: simplify both sides of the equation.

5=812a+9+3

5=(812a)+(9+3)(combine like terms)

5=812a+12

5=812a+12

step 2: flip the equation.

812a+12=5

step 3: subtract 12 from both sides.

812a+12−12=5−12

812a=−7

step 4: divide both sides by 812.

812a /812 = -7/812

a= -1/116

so the answer is

a=   -1/116