Question

a coin is tossed and a six - sided die numbered 1 through 6 is rolled. find the probability of tossing a tail and then rolling a number greater than 2. (round to three decimal places as needed.)

Explanation:

Step1: Find probability of getting 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.
$P(T)=\frac{1}{2}=0.5$

Step2: Find probability of rolling a number greater than 2 on a six - sided die

A six - sided die has numbers 1, 2, 3, 4, 5, 6. The numbers greater than 2 are 3, 4, 5, 6. So there are 4 favorable outcomes out of 6 possible outcomes. The probability of rolling a number greater than 2, $P(N>2)$, is $\frac{4}{6}=\frac{2}{3}\approx0.667$

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 the product of their individual probabilities. Let $P$ be the probability of tossing a tail and then rolling a number greater than 2. Then $P = P(T)\times P(N > 2)$
$P=0.5\times\frac{2}{3}=\frac{1}{3}\approx0.333$

Answer:

$0.333$