a coin is flipped, then a number cube is rolled. the tree diagram shows the possible outcomes. what is…

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

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

Answer

Explanation:

Step1: Find probability of heads

A coin has 2 sides. Probability of getting heads, $P(H)=\frac{1}{2}$.

Step2: Find probability of rolling a 2

A number - cube has 6 sides. Probability of rolling a 2, $P(2)=\frac{1}{6}$.

Step3: Use multiplication rule for independent events

Since coin - flip and cube - roll are independent, $P(H,2)=P(H)\times P(2)$. $P(H,2)=\frac{1}{2}\times\frac{1}{6}=\frac{1}{12}$

Answer:

$\frac{1}{12}$