Question

Let X ∼ B(1/4) and Y be a fair six sided dice roll, and assume they are independent. Write down the probability density (sometimes called mass) function for (X, Y ). What is the probability that you flip a heads and roll a five or higher?

Answer 1

The probability of flipping a heads and rolling a five or higher is 1/12.

Step-by-step explanation:

To find the probability of flipping a heads and rolling a five or higher, we need to consider the probabilities of these two events separately and then multiply them together. Let's start with flipping a heads. The random variable X follows a binomial distribution with a probability of success (heads) of 1/4. Since there is only one flip, the probability of getting a heads is 1/4.

Next, let's consider the probability of rolling a five or higher on a fair six-sided die. The event of rolling a five or six has a probability of 2/6, or 1/3.

To find the probability of both events occurring, we multiply the probabilities together: P(X=1) * P(Y>=5) = 1/4 * 1/3 = 1/12.