Question

a coin is tossed and an eight - sided die numbered 1 through 8 is rolled. find the probability of tossing a tail and then rolling a number greater than 2. the probability of tossing a tail and then rolling a number greater than 2 is
(round to three decimal places as needed.)

Explanation:

Step1: Calculate the probability of tossing a tail

A coin has 2 sides (head and tail). The probability of getting a tail, \(P(T)\), is \(\frac{1}{2}\) since there is 1 favorable outcome (tail) out of 2 possible outcomes (head or tail).

Step2: Calculate the probability of rolling a number greater than 2 on an eight - sided die

An eight - sided die has numbers 1 - 8. The numbers greater than 2 are 3, 4, 5, 6, 7, 8. So there are 6 favorable outcomes. The probability of rolling a number greater than 2, \(P(N>2)\), is \(\frac{6}{8}=\frac{3}{4}\)

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 \(P = P(T)\times P(N > 2)\)
Substitute the values: \(P=\frac{1}{2}\times\frac{3}{4}=\frac{3}{8}=0.375\)

Answer:

\(0.375\)