Marcus flips a coin and tosses a six-sided die with the sides numbered 1 through 6. What is the probability that he gets a head on the coin and a number divisible by 3 on the die
Head = 1/2
3 or 6 = 1/6 + 1/6 = 1/3
Probability of both/all events occurring is found by multiplying the individual probabilities.
To find the probability that Marcus gets a head on the coin and a number divisible by 3 on the die, we need to determine the number of favorable outcomes and the total number of possible outcomes.
First, let's consider the coin toss. There are two possible outcomes, a head (H) or a tail (T). Since we are interested in the probability of getting a head, there is only one favorable outcome.
Next, let's consider the die. There are six possible outcomes, numbers 1, 2, 3, 4, 5, or 6. We want to find the probability of getting a number divisible by 3, which in this case would be 3 or 6. There are two favorable outcomes (3 and 6) out of the six possible outcomes.
To find the overall probability, we need to multiply the probabilities of both events occurring. Since each event is independent, we can multiply the individual probabilities together.
Probability of getting a head on the coin: 1/2
Probability of getting a number divisible by 3 on the die: 2/6 = 1/3
Now, multiply these probabilities:
(1/2) * (1/3) = 1/6
Therefore, the probability that Marcus gets a head on the coin and a number divisible by 3 on the die is 1/6.