Final answer:
To find the odds against an event, calculate the probability of the event not occurring and divide it by the probability of the event occurring. Given that events E and F are independent, we can use the formula P(E|F) = P(E) - P(E and F) to find the probability of event E given that event F has occurred. The odds against event E are 3 : 2.
Step-by-step explanation:
To find the odds against an event, we need to calculate the probability of the event not occurring and then divide it by the probability of the event occurring.
Given that events E and F are independent, we can use the formula P(E|F) = P(E) - P(E and F) to find the probability of event E given that event F has occurred.
Since the events are independent, P(E and F) = P(E) * P(F). Substituting the given values, we have P(E|F) = 0.4 - (0.4)(0.5) = 0.4 - 0.2 = 0.2.
To calculate the odds against event E, we need to find the probability of not E, which is 1 - P(E). Therefore, the odds against event E are (1 - P(E)) / P(E) = (1 - 0.4) / 0.4 = 0.6 / 0.4 = 3 : 2.