60% of the hockey players are from Eastern Canada and 40% are from Western Canada. 18% of the Eastern players and 12% of the Western players go on to play in the NHL. If a randomly chosen NHL player is selected, what is the probability that he is from Western Canada?

Question

60% of the hockey players are from Eastern Canada and 40% are from Western Canada. 18% of the Eastern players and 12% of the Western players go on to play in the NHL. If a randomly chosen NHL player is selected, what is the probability that he is from Western Canada?

P(NHL|W)=(0.4x0.12)/(0.4x0.12)(0.18x0.6) ?

Answer 1

Your answer tells me that you are in the right direction, but there is something wrong with the expression:

(0.4x0.12)/(0.4x0.12)(0.18x0.6)
because it evaluates to 9.259 > 1.

Think of a bag of 4 red and 6 blue marbles. The chances of drawing a red would be
4/(4+6)=0.4.

Rework your expression and I am sure you'll get the right answer.

Answer 2

yes,y ou have it right

say there are 100 total
60 E
40 W
E in NHL = .18*60 = 10.8
W in NHL = .12*40 = 4.8
Total = 10.8+4.8 = 15.6
fraction W in total = 4.8/15.6

Answer 3

Oh, but you multiplied on the bottom instead of adding.

Answer 4

Whoops, a typo. I finally got one of these questions right :)

Thank you!

Answer 5

To find the probability that a randomly chosen NHL player is from Western Canada, we need to use conditional probability.

Let's break down the problem step by step:

1. We are given that 60% of hockey players are from Eastern Canada, which means that the remaining 40% must be from Western Canada.
P(E) = 0.6 (probability of Eastern player)
P(W) = 0.4 (probability of Western player)

2. We are also given that 18% of Eastern players and 12% of Western players make it to the NHL.
P(NHL|E) = 0.18 (probability of being an NHL player given they are from Eastern Canada)
P(NHL|W) = 0.12 (probability of being an NHL player given they are from Western Canada)

3. Now, we want to find the probability that a randomly chosen NHL player is from Western Canada.
We can use Bayes' Theorem to calculate this:
P(W|NHL) = P(NHL|W) * P(W) / P(NHL)

P(NHL) can be calculated by using the Law of Total Probability:
P(NHL) = P(NHL|E) * P(E) + P(NHL|W) * P(W)

Now, let's substitute the given values into the formulas:
P(NHL|W) = 0.12
P(W) = 0.4
P(E) = 0.6
P(NHL|E) = 0.18

P(NHL) = P(NHL|E) * P(E) + P(NHL|W) * P(W)
= 0.18 * 0.6 + 0.12 * 0.4

After calculating P(NHL), we can substitute all the values back into the original formula:
P(W|NHL) = P(NHL|W) * P(W) / P(NHL)

Now, you can plug in the values to calculate the probability that a randomly chosen NHL player is from Western Canada.