Question

a coin is flipped, then a number cube is rolled. the tree diagram shows the possible outcomes. what is p(heads, then 2)? 1/12 1/6 7/12 5/6

Explanation:

Step1: Calculate the probability of getting heads

The probability of getting heads when flipping a coin is \(P(\text{heads})=\frac{1}{2}\) since there are 2 possible outcomes (heads or tails).

Step2: Calculate the probability of rolling a 2

The probability of rolling a 2 on a number cube (which has 6 possible outcomes \(1 - 6\)) is \(P(2)=\frac{1}{6}\)

Step3: Use the multiplication rule for independent events

For two independent events \(A\) and \(B\), \(P(A\text{ and }B)=P(A)\times P(B)\). Here, \(A\) is getting heads and \(B\) is rolling a 2. So \(P(\text{heads, then }2)=\frac{1}{2}\times\frac{1}{6}\)

$$ \frac{1}{2}\times\frac{1}{6}=\frac{1\times1}{2\times6}=\frac{1}{12} $$

Answer:

\(\frac{1}{12}\) (the first option)