Probability Question - P(A n B n C)?

Question

There are 5 horses (A,B,C,D,E).
Each has an equal chance of placing first in a race (20%).
What is the probability that a punter will win a trifector in a bet (that is, the punter will successfully guess who will place 1, 2, and 3.)?

It would help me greatly if you could explain the formula.

I know that the probability of the punter guessing who will place 1 & 2 is just "P(A n B) = P(A)xP(B)." I thought maybe that means the formula for "P(A n B n C) = P(A)xP(B)xP(C)" but this doesn't seem to be correct. Thanks for any help.

Answer 1

Break it up into parts. The probability of guessing who is first is 20%. Then there is a 25% chance of guessing who is second. Finally there is a 33% chance of guessing who is third.

Another way to do it would be to know that there are 5x4x3x2x1 possibilites for outcomes of the race. A fifth of those would have the horse you chose as first. A fourth of those (or a twentieth of the total) would have the correct horse in second. Finally, a third of those (or one sixtieth of the total) would have the correct third place finisher.

So your answer would be 1/60.

Answer 2

variety of. There are 92 evidently going on ingredient son earth. At one time there have been extra, yet all components heavier than 92, are radioactive, and consequently subject to radioactive decay. components like Plutonium (#ninety 4) probable existed very early on, yet with a one million/2 lifestyles of basically some thousand years, each and all the unique plutonium has decayed into different components. basically about all plutonium in the worldwide now could be formed synthetically via bombarding lighter components with helium nuclei. All components heavier than iron can basically be formed in super novae. on a similar time because it is for particular that super novae produce components heavier than Uranium, and particular even heavier than #118, those components have very short one million/2 lives and would disappear almost immediately after their creation. So in different words, there are no components different than the ninety 4 evidently going on components that exist in the universe with any abundance. As on your questions approximately extra beneficial-terrestrial civilizations, even however there technologies and biology would probably be very distinctive, it would probable be produced from the comparable chemical components. components like carbon, nitrogen, oxygen, hydrogen, and silicon, are the main effortless components in the universe. it is not any marvel that those at the instant are not basically the development blocks of all lifestyles as all of us comprehend it, yet that components like silicon are used to make electronics. There abundance makes their use useful.

Answer 3

There are 5C3 = 10 combinations of trifectas.
p(w) = (1/10)(1/5)(1/4)(1/3) = 1/600