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xleb123 · Accepted Answer

To construct the probability distributions for the given data, we need to calculate the probabilities of randomly selecting each type of bill.
Let's denote the random variables as follows:
- X₁: Number of 100 peso bills
- X₂: Number of 200 peso bills
- X₃: Number of 500 peso bills
- X₄: Number of 1 000 peso bills
We are given the following information:
- Five 100 peso bills
- Four 200 peso bills
- Three 500 peso bills
- Two 1 000 peso bills
To calculate the probabilities, we divide the number of bills of each type by the total number of bills. In this case, the total number of bills is 5 + 4 + 3 + 2 = 14.
The probability distribution for X₁ (the number of 100 peso bills) is as follows:

P (X ₁ = 0) = \frac{5}{14}

P (X ₁ = 1) = \frac{5}{14}

P (X ₁ = 2) = \frac{5}{14}

P (X ₁ = 3) = \frac{5}{14}

P (X ₁ = 4) = \frac{5}{14}

P (X ₁ = 5) = \frac{5}{14}

The probability distribution for X₂ (the number of 200 peso bills) is as follows:

P (X ₂ = 0) = \frac{6}{14}

P (X ₂ = 1) = \frac{6}{14}

P (X ₂ = 2) = \frac{6}{14}

P (X ₂ = 3) = \frac{6}{14}

P (X ₂ = 4) = \frac{6}{14}

The probability distribution for X₃ (the number of 500 peso bills) is as follows:

P (X ₃ = 0) = \frac{11}{14}

P (X ₃ = 1) = \frac{11}{14}

P (X ₃ = 2) = \frac{11}{14}

The probability distribution for X₄ (the number of 1 000 peso bills) is as follows:

P (X ₄ = 0) = \frac{12}{14}

P (X ₄ = 1) = \frac{12}{14}

These probability distributions represent the chances of randomly selecting a certain number of bills of each type from your wallet.
For example, the chance of randomly selecting a 100 peso bill is

\frac{5}{14}

, a 200 peso bill is

\frac{6}{14}

, a 500 peso bill is

\frac{11}{14}

, and a 1 000 peso bill is

\frac{12}{14}

.

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