You flip a coin and then roll a fair six-sided number cube. What is the probability the coin lands heads-up and the number cube shows a number 3?
A) 1/2
B) 1/3
C) 1/6
D) 1/12
To find the probability that the coin lands heads-up and the number cube shows a number 3, we need to multiply the probabilities of each event occurring.
The probability of the coin landing heads-up is 1/2, since there are two equally likely outcomes (heads or tails) and only one of them is heads.
The probability of the number cube showing a 3 is 1/6, since there are six equally likely outcomes (numbers 1 to 6) and only one of them is a 3.
To find the combined probability, we multiply 1/2 by 1/6:
(1/2) * (1/6) = 1/12
Therefore, the probability that the coin lands heads-up and the number cube shows a number 3 is 1/12.
The answer is D) 1/12.
To find the probability of two independent events happening, you need to multiply the probabilities of each event separately.
First, let's find the probability of getting heads on the coin flip. Since it is a fair coin, there are two equally likely outcomes: heads or tails. So, the probability of getting heads is 1/2.
Next, let's find the probability of rolling a number 3 on the six-sided number cube. Since there are six equally likely outcomes (numbers 1 to 6), and only one of them is a 3, the probability of rolling a 3 is 1/6.
To find the probability of both events happening (coin lands heads up AND number cube shows a 3), you multiply the probabilities. Therefore, the probability is (1/2) * (1/6) = 1/12.
So, the correct answer is D) 1/12.
You are dealing with independent events, that is, the die does not know, care or affect what the coin is doing.
So multiply the probabilities of each of the two events.