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Answer: Choice C) 9/100</h3>
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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.
