Given the following table provides a probability distribution for the random variable $X$:

$X$	$P\left(X\right)$
1	0.2
2	0.5
3	0.3

Which of the following statements is true about this probability distribution?

• A. The probability of $X$ being 2 is less than the probability of $X$ being 1.
• B. The sum of all probabilities is equal to $1$.
• C. The probability of $X$ being 3 is the highest among all values.
• D. The sum of all probabilities is greater than $1$.

Answer: (B)

Verified step by step guidance

1. Identify the probabilities given for each value of the random variable \(X\): \(P(X=1) = 0.2\), \(P(X=2) = 0.5\), and \(P(X=3) = 0.3\).
2. Recall that for any probability distribution, the sum of all probabilities must equal 1. This is a fundamental property of probability distributions.
3. Calculate the sum of the given probabilities: \$0.2 + 0.5 + 0.3$.
4. Compare the individual probabilities to determine which is the highest: check if \(P(X=3)\) is greater than \(P(X=1)\) and \(P(X=2)\).
5. Evaluate the statements based on your calculations: verify if the sum equals 1, if any probability is less than another, and if the sum is greater than 1.