Question

ten people (labeled 1-10) have purchased raffle tickets for a fundraiser. however, they did not all purchase the same number of tickets. one ticket is to be selected at random. which of the following could be the probability distribution for the winning ticket?

Explanation:

Step1: Check the properties of probability distribution

A probability distribution must satisfy two conditions:

1. Each probability \(P(x)\) is between \(0\) and \(1\) (i.e., \(0\leq P(x)\leq1\)).
2. The sum of all probabilities \(\sum_{i = 1}^{n}P(x_i)=1\).

Step2: Analyze each option

• First option:

Sum of probabilities \(=0.10\times10 = 1\), and each probability \(0.10\) is between \(0\) and \(1\). But the problem states “they did not all purchase the same number of tickets”, so this uniform distribution is not valid.

• Second option:

Sum of probabilities \(=0.01 + 0.01+0.05 + 0.07+0.68+0.01+0.05+0.03+0.01+0.08=1.0\). But we assume non - uniform (since not same number of tickets), but let's check other options.

• Third option:

Sum of probabilities \(=0.01+0.11 + 0.02+0.12+0.03+0.13+0.04+0.14+0.05+0.15\)

$$
LATEXBLOCK0
$$

Sum \(= 0.8
eq1\), so this is not a probability distribution.

• Fourth option:

There is a probability \(- 0.125\) which is less than \(0\). So this is not a probability distribution.

Answer:

The second option (with values \(0.01,0.01,0.05,0.07,0.68,0.01,0.05,0.03,0.01,0.08\)) could be the probability distribution (assuming the non - uniform nature as per the problem statement, and it satisfies \(0\leq P(x)\leq1\) and \(\sum P(x)=1\))