Questions: If the probability that an identified hurricane will make a direct hit on a certain stretch of beach is 0.01, what are the odds against a direct hit? A. 100 to 1 B. 99 to 1 C. 98 to 1 D. 1 to 100

Solution Steps

To find the odds against a direct hit, we need to understand the relationship between probability and odds. The probability of an event happening is given, and the odds against the event are calculated as the ratio of the probability of the event not happening to the probability of the event happening.

Given:

• Probability of a direct hit (P) = 0.01

The probability of the event not happening (Q) is:

• Q = 1 - P

The odds against the event are then:

• Odds against = Q : P

The probability of a direct hit by the hurricane is given as: \[ P = 0.01 \]

The probability of not having a direct hit is calculated as: \[ Q = 1 - P = 1 - 0.01 = 0.99 \]

The odds against a direct hit are given by the ratio of the probability of no direct hit to the probability of a direct hit: \[ \text{Odds against} = \frac{Q}{P} = \frac{0.99}{0.01} = 99 \] Thus, the odds against a direct hit can be expressed as: \[ \text{Odds against} = 99 : 1 \]

Final Answer