In endurance horse racing, people over the age of 15 are called seniors and people 15 years or younger are called juniors. An endurance horse race consists of 25 seniors and 8 juniors. (Give answer as a fraction or a decimal out to at least 4 places. If your answer is very small use scientific notation for example 3.3421E-6.)
So there are a total of 25+ 8= 33 horses.
What is the probability that the top three finishers were:
(a) all seniors
The probability the first horse is a senior is 25/33. There are then 32 horses left, 24 of them seniors. The probability the second horse is also a senior is 24/32. There are then 31 horses left, 23 of them seniors. The probability the third horse is also a senior is 23/31. The probability all three finishers is (25/33)(24/32)(23/31)= 0.42, approximately. That's not "very small".
Try this yourself this the same way as above.
(c) 2 seniors and 1 junior
A little bit different. The probability the first horse is a senior is 25/33 and the probability the second horse is a senior is 24/32 as above. There are then 31 horses, 8 of them juniors. The probability the third horse is a junior is 8/31. The probability the first and second horses are seniors and the third is a junior ("senior, senior, junior") is (25/33)(24/32)(8/31). But "2 seniors and 1 junior" could also be "senior, junior, senior". The probability the first horse is a senior is 25/33 as above. Then there are 32 horses, 8 of them juniors, so the probability the second horse is a junior is 8/32. Then there are 31 horses, 24 of them seniors so the probability the third horse is a senior is 24/31. The probability of (senior, junior, senior) in
that order is (25/33)(8/32)(24/31). You should see that this is really the same number- just with the numerators in different order. Similarly the probability of (junior, senior, senior) is also (8/33)(25/32)(24/31), again the same number. The probability of two seniors and one junior is 3(25/33)(24/32)(8/31).
(d) 1 senior and 2 juniors
Try this now, the same as in the previous problem.
I am really stuck with this concept, can you show the steps and how it was completed