Final Answer:
The probability that Justin is president and Ivanna is vice president is 1/15.
Step-by-step explanation:
The probability of independent events occurring together is calculated by multiplying their individual probabilities. In this case, the probability of Justin becoming president is 1/5, and the probability of Ivanna becoming vice president is 1/3. To find the probability of both events happening, multiply the two probabilities: (1/5) * (1/3) = 1/15.
In probability, each event's outcome is unaffected by the occurrence or non-occurrence of the other. Justin's presidency and Ivanna's vice presidency are independent events because one does not influence the other. The reduced fraction, 1/15, represents the likelihood of both events happening concurrently.
It's crucial to understand the concept of independence when dealing with probability. In this scenario, the assumption is that the chances of Justin being president do not impact the chances of Ivanna being vice president, and vice versa. Therefore, the probability of their joint occurrence is the product of their individual probabilities, resulting in the final answer of 1/15.