Experts calculate the probability of a particular horse winning the Kentucky Derby to be $P($ win $)=0.25$.
What is the probability (in decimal form) that the horse will not win the race? $P($ not win) $=$
What are the odds against the horse winning the race? to Simplify your answers.
Answer
Final Answer: The probability that the horse will not win the race is \(\boxed{0.75}\). The odds against the horse winning the race are \(\boxed{3:1}\).
Step 1 ：The probability of a particular horse winning the Kentucky Derby is given as \(P(\text{win}) = 0.25\).
Step 2 ：The probability of an event not happening is 1 minus the probability of the event happening. Therefore, the probability of the horse not winning is \(1 - P(\text{win})\).
Step 3 ：Substituting the given value, we get \(P(\text{not win}) = 1 - 0.25 = 0.75\).
Step 4 ：The odds against an event are the ratio of the probability of the event not happening to the probability of the event happening. Therefore, the odds against the horse winning are \(\frac{P(\text{not win})}{P(\text{win})}\).
Step 5 ：Substituting the calculated values, we get odds against = \(\frac{0.75}{0.25} = 3.0\).
Step 6 ：Final Answer: The probability that the horse will not win the race is \(\boxed{0.75}\). The odds against the horse winning the race are \(\boxed{3:1}\).
