Question

If two coins are selected at random without replacement from the box containing a penny, two nickels, and a dime, what is the probability density function of the sum of the values of the two coins, denoted as x?

a) P(x = 0) = 1/6
b) P(x = 5) = 1/3
c) P(x = 10) = 1/6
d) P(x = 15) = 0

Answer 1

The probability density function (PDF) of the sum of two coins can be calculated by considering all possible outcomes. The PDF for this scenario is:

• P(x = 0) = 0
• P(x = 5) = 1/6
• P(x = 10) = 1/12
• P(x = 15) = 1/6
• For any other value of x, the probability is 0.

Step-by-step explanation:

The probability density function (PDF) of the sum of the values of two coins can be calculated by considering all possible outcomes. In this case, we have a penny, two nickels, and a dime in the box. Let's break down the possible outcomes:

1. Choosing a penny and a nickel: probability = (1/4) * (2/3) = 1/6
2. Choosing a penny and a dime: probability = (1/4) * (1/3) = 1/12
3. Choosing a nickel and a dime: probability = (2/4) * (1/3) = 1/6

Summing up these probabilities, we find the PDF:

• P(x = 0) = 0
• P(x = 5) = 1/6
• P(x = 10) = 1/12
• P(x = 15) = 1/6
• For any other value of x, the probability is 0.