6. Carlos flips a coin 80 times, then rolls a number cube 80 times. His results are shown in the tables below. Based on Carlos’s results, what is the experimental probability that the next time he flips the coin and rolls the cube, the coin will land tails-up and the number cube will land on 2?

Explanation:

We have these two events

The experimental (aka empirical) probabilities of each are

Note how P(A) is not 1/2 like we expect; however it's fairly close because 9/20 = 0.45 while 1/2 = 0.5 in slight contrast. The experimental probability never 100% lines up with the theoretical probability, but will get closer as you do more trials (due to the law of large numbers). A similar situation happens with P(B). The theoretical probability would be P(B) = 1/6 = 0.1667

Events A and B are independent, which allows us to multiply the probabilities:

P(A and B) = probability of getting tails and rolling a '2'

P(A and B) = P(A)*P(B)

P(A and B) = (9/20)*(1/5)

P(A and B) = (9*1)/(20*5)

P(A and B) = 9/100 which points the answer to choice C

Slight alternative method:

P(A and B) = P(A)*P(B) = (36/80)*(16/80) = 0.09 = 9/100

this method involves typing (36/80)*(16/80) into your calculator.

step-by-step explanation:

there is a formula i can give you:

it is r^2*n*sin(360/n) divided by 2 where r represents the "radius" and n is the number of sides.

plug them in:

(10sqrt(3))^2*6*sin(360/6) divided by 2

100*3*6*sin(60) divided by 2

900*sin(60)

900*sqrt(3)/2

450*sqrt(3)

approx is 779.4 cm^2