Suppose that you toss a coin and roll a die. What is the probability of obtaining each of the following combinations? (Enter your answers as fractions.)
P(Tails or a Five)
If the events are independent, the probability of both/all events occurring is determined by multiplying the probabilities of the individual events.
P = 1/2 * 1/6 = ?
If the events are independent, the probability of both/all events occurring is determined by multiplying the probabilities of the individual events.
I assume you meant tails AND a five.
P = 1/2 * 1/6 = ?
Either-or probabilities are found by adding the individual probabilities.
To find the probability of obtaining either a tails or a five, we need to calculate the probability of each event separately and then add the probabilities together.
First, let's find the probability of getting tails. When flipping a fair coin, there are two equally likely outcomes: heads or tails. So the probability of getting tails is 1 out of 2, which can be written as 1/2.
Next, let's find the probability of rolling a five on a fair six-sided die. The die has six equally likely outcomes, which are the numbers from 1 to 6. Since we want to find the probability of rolling a five, which is only one of these numbers, the probability is 1 out of 6, or 1/6.
Finally, to find the probability of obtaining either a tails or a five, we add the probabilities of the individual events. So the probability is:
P(Tails or a Five) = P(Tails) + P(Five) = 1/2 + 1/6 = 3/6 + 1/6 = 4/6 = 2/3
Therefore, the probability of obtaining either a tails or a five is 2/3.