How do you find the probability of 4 blue marbles 5 red marbles 1 green marble and 2 black marbles?

Answer 1

It depends what probability exactly you want to find.

probability = number of successful ways / total number of ways

If the problem is:

You have a bag containing 4 blue, 5 red, 1 green, 2 black marble what is the probability of picking a blue marble at random?

Then

successful ways = 4 as there are 4 blue marbles

total ways = 12 as there are 4 [blue] marbles + 5 [red] marbles + 1 [green] marble + 2 [black] marbles = 12 marbles in total.

pr(picking a blue) = 4/12 = 1/3

Perhaps the problem is:

You pick 2 marbles at random without replacing them, what is the probability that they are the two black marbles?

Each picking of a marble is an event and the two events are independent (in the sense that whatever you pick first does not affect the probability of the second pick) so you multiply the probability of each together:

pr(1st black) = 2/12 = 1/6

pr(2nd black) = 1/11 (there is 1 less black marble in the bag)

pr(2 blacks) = 1/6 × 1/11 = 1/66

Perhaps it is:

You pick 2 marbles at random replacing the marble after the first pick, what is the probability of picking the same colour each time?

This time there are 4 possible colours and the probabilities of 2 marbles the same is calculated for each (similar to above) and then they are added together to find the total probability of 2 marbles of the same colour:

pr(blue) = 4/12 → pr(2 blue) = 4/12 × 4/12 = 16/144

pr(red) = 5/12 → pr(2 red) = 5/12 × 5/12 = 25/144

pr(green) = 1/12 → pr(2 green) = 1/12 × 1/12 = 1/144

pr(black) = 2/12 → pr(2 black) = 2/12 × 2/12 = 4/144

→ pr(2 the same colour) = pr(2 blue) + pr(2 red) + pr(2 green) + pr(2 black)

= 16/144 + 25/144 + 1/144 + 4/144 = 46/144 = 23/72

And so on.