Question

6. Carlos flips a coin 80 times, then rolls a number cube 80 times. His results are shown in the tables below.

Answer 1

Answer:   Choice C)    9/100

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Explanation:

We have these two events

• A = the coin lands on tails
• B = the number cube (aka dice) lands on '2'

The experimental (aka empirical) probabilities of each are

• P(A) = 36/80 = 9/20
• P(B) = 16/80 = 1/5

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

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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.