if you toss a coin and roll a number cube, what is the probability of obtaining a head and rolling a 6…

Explanation:

Step1: Find probability of getting a head

The probability of getting a head when tossing a fair - coin is $P(H)=\frac{1}{2}$ since there are 2 possible outcomes (head or tail) and 1 favorable outcome (head).

Step2: Find probability of rolling a 6

The probability of rolling a 6 on a fair six - sided number cube is $P(6)=\frac{1}{6}$ since there are 6 possible outcomes (1, 2, 3, 4, 5, 6) and 1 favorable outcome (6).

Step3: Use the multiplication rule for independent events

Since the coin - toss and the number - cube roll are independent events, the probability of both events occurring is the product of their individual probabilities. So $P(H\cap6)=P(H)\times P(6)$. Substitute $P(H)=\frac{1}{2}$ and $P(6)=\frac{1}{6}$ into the formula: $P(H\cap6)=\frac{1}{2}\times\frac{1}{6}=\frac{1}{12}\approx0.08$.

Answer:

$0.08$