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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

User Doldt
by
7.6k points

1 Answer

5 votes

Final answer:

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.

User Ion Scerbatiuc
by
8.0k points
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