Question

a coin is tossed and an eight - sided die numbered 1 through 8 is rolled. find the probability of tossing a head and then rolling a number greater than 6. the probability of tossing a head and then rolling a number greater than 6 is (round to three decimal places as needed.)

Explanation:

Step1: Calculate the probability of tossing a head

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

Step2: Calculate the probability of rolling a number greater than 6 on an eight - sided die

The numbers greater than 6 on an eight - sided die (numbered 1 - 8) are 7 and 8. So there are 2 favorable outcomes out of 8. Then \(P(\text{number}>6)=\frac{2}{8}=\frac{1}{4}\)

Step3: Use the multiplication rule for independent events

Since the coin toss and die roll are independent events, the probability of both events occurring is \(P = P(\text{head})\times P(\text{number}>6)\)
Substitute the values: \(P=\frac{1}{2}\times\frac{1}{4}=\frac{1}{8}= 0.125\)

Answer:

\(0.125\)