A coin is tossed and die is rolled. What is the probability of getting a tails and then rolling a 5?
1/2 * 1/6 = 1/12
independent events ... multiply the individual probabilities
p(t) = 1/2 ... p(5) = 1/6
p(t & 5) = ?
To find the probability of getting a tails and then rolling a 5, we need to multiply the probability of each event occurring.
Let's start with the coin toss. When tossing a fair coin, there are two equally likely outcomes: heads or tails. Therefore, the probability of getting a tails is 1/2.
Next, let's consider the roll of a die. A standard die has six sides, numbered from 1 to 6. Therefore, the probability of rolling a 5 is 1/6.
To find the probability of both events occurring, we multiply these probabilities together:
Probability of getting tails and rolling a 5 = Probability of getting tails * Probability of rolling a 5
= 1/2 * 1/6
= 1/12
So, the probability of getting a tails and then rolling a 5 is 1/12.