Question

HELP WITH PROBABILITY. in the group of athletes, 20 skiers, cyclists 5 and 4 runners. Probability to perform discharge as follows: for the skier 0.9: 0.8 for the cyclist: 0.75 for the runner. Athlete, are caused by random, fulfilled the norm. Find the probability that he was involved in cycling.

Answer 1

You have this information:
29 athletes. -> P(ski) = 20/29, P(cycling) = 5/29, P(runner) = 4/29.
P(ok|ski) = 0.9
P(ok|cycling) = 0.8
P(ok|running) = 0.75

You want: P(cycling|ok).

Do you have a clue about what formula is needed?

Answer 2

what does ok mean ?

Answer 3

ok = "fulfill the norm"

Answer 4

oh, i see.

Answer 5

there's a formula that helps you switch events like this: P(fulfil|cycler) = P(cycle|fulfil) * .... / ....
The name starts with a 'B'.

Answer 6

Bayes's formula, know this one?

Answer 7

yeah, i know the formula. Thanks.

Answer 8

@reemii could you help me how to use bayes' formula with this one ?

Answer 9

I know the formula but kind of confused how to make this work with the question.

Answer 10

yes. Let's use some letters: C : Cycling, S : Ski, R : Running, F : Fulfill the norm.
\[ P(C | F) = \frac{P(F|C)P(C)}{P(F|S)P(S)+P(F|C)P(C)+P(F|R)P(R)} \]

Answer 11

Thank you.

Answer 12

and we know
\[P(F|S) = 0.9\\ P(F|C) = 0.8 \\P(F|R) = 0.75\]
Furthermore, an athlete chosen at random has a 20/29 probability to be a skier, etc...

Answer 13

yes, that's a given.

Answer 14

P(S)=20/29, P(C)=5/29, P(R)=4/29. So, 0.16 ?

Answer 15

\[ P(C | F) = \frac{0.8 \cdot (5/29)}{0.9 \cdot (20/29)+0.8\cdot (5/29) + 0.75 \cdot (4/29)} = 0.16\]

Answer 16

yeah, i got that :D