What is the probability that an event will not occur when the odds that it will occur are 4 to 5?

• A. Four Ninths (4/9)
• B. Five Ninths (5/9)
• C. Three Fifths (3/5)
• D. Two Fifths (2/5)

Answer: (B)

To find the probability that an event will not occur given the odds that it will occur are 4 to 5, we first need to understand how odds translate to probability. Odds of 4 to 5 imply that for every 4 occurrences of an event, there are 5 non-occurrences.

To express this in terms of probability, we can think of the total occurrences as the sum of the favorable and unfavorable outcomes: 4 (the event occurs) + 5 (the event does not occur) = 9 total outcomes. The probability of the event occurring can therefore be calculated as the ratio of the occurrences of the event to the total outcomes:

Probability of the event occurring = Number of occurrences / Total outcomes = 4 / 9.

The probability of the event not occurring is then found by subtracting the probability of the event occurring from 1:

Probability of not occurring = 1 - Probability of occurring = 1 - 4/9 = 5/9.

This aligns with the understanding of probability as a measure of the likelihood of an event happening versus it not happening. Thus, the probability that the event will not occur, given the odds of 4 to 5, is accurately represented as five ninths