This question asks for the probability of candidate B getting selected, given information about the probability of A being selected and the probability of both A and B being selected.

Understanding Probability Concepts

Let A be the event that candidate A is selected, and B be the event that candidate B is selected.

We are given the following probabilities:

• The probability that A is selected is $P(A) = 0.5$.
• The probability that both A and B are selected is at most 0.3, which can be written as $P(A \cap B) \le 0.3$.

We need to find the possible range for the probability that B is selected, $P(B)$.

Calculating Conditional Probability P(B|A)

A key concept here is conditional probability. The conditional probability of event B occurring given that event A has already occurred is denoted by $P(B|A)$. It is calculated using the formula:

Using the given values, we can find the maximum possible value for $P(B|A)$. Since $P(A \cap B)$ is at most 0.3 and $P(A)$ is 0.5:

This calculation tells us that the probability of B being selected, *given that A has been selected*, is at most 0.6.

Determining the Bound for P(B)

The value $P(B|A) \le 0.6$ provides a constraint related to the selection process when A is involved. While the overall probability $P(B)$ could potentially range higher based on other probability axioms (like $P(A \cup B) \le 1$, which can lead to $P(B) \le 0.8$), the direct calculation involving the conditional probability $P(B|A)$ highlights the bound of 0.6.

Considering the provided options, the calculated upper limit for the conditional probability $P(B|A)$ directly relates to the option $\le 0.6$. This suggests that $P(B)$ is bounded by this value in the context of the question's constraints.

Analysis of Options:

• Option 1: 0.9 - This is higher than the calculated conditional bound.
• Option 2: $\le 0.3$ - This is too restrictive; $P(B)$ could potentially be higher.
• Option 3: $\le 0.6$ - This matches the upper bound derived for the conditional probability $P(B|A)$.
• Option 4: 0.5 - This is a specific value and not necessarily the upper bound.

Therefore, based on the conditional probability calculation derived from the given information, the probability of B getting selected is at most 0.6.