Maths Probability Question?

2/6x1/5=2/30 or 1/15

The conventional way to figure this out is to figure the probability of drawing two red balls, two green balls or two blue balls and add them all up.

At the beginning you have 2 red balls out of 6 total:

P(first is red) = 2/6 = 1/3

Once that is removed, you have 1 red ball out of 5 total:

P(second is red) = 1/5

The probability of both events is the product:

P(both red) = 1/3 * 1/5 = 1/15

If you repeat this process for two greens or two blues, you get the same results. So the total probability is:

P(same color) = 1/15 + 1/15 + 1/15

= 3/15

= 1/5

However there's a much quicker way to get to the same result – notice that the colors are equally distributed. So you are equally likely to pick red, green or blue on the first draw. That leaves you with 1 ball that matches out of 5 remaining balls. So you can directly get to the answer of 1/5 that the second ball matches the first and this they are the same color.

Answer:

1/5

p(2 balls same color) =

p(2 red or 2 green or 2 blue) =

p(2 red) + p(2 green) +p(2 blue) =

(p(1st is red) * p(2nd is red)) + (p(1st is green) * p(2nd is green)) + (p(1st is blue) * p(2nd is blue))

(2/6 * 1/5) + (2/6 * 1/5) + (2/6 * 1/5) =

3(2/6 * 1/5) =

1/5

P (red and red) = 2/6 x 1/5 = 1/15

P (green and green) = 2/6 x 1/5 = 1/15

P (blue and blue) = 2/6 x 1/5 = 1/15

P (same color) = 3/15 = 1/5

Regardless of the color of the first ball chosen, there will remain five balls, one of which matches the color already chosen.

P(1st red ball) = 2 red balls/total 6 balls = 2/6 = ⅓

P(2nd red ball) = 1 remaining red ball / total 5 remaining balls = ⅕

So P( both red balls) = ⅓ x ⅕ = 1/15

Similarly since both green and blue balls are also 2, we get

P(both green balls) = 1/15

P(both blue balls) = 1/15

Now P( both same colour) = P(both red balls) + P(both green balls) + P(both blue balls)

P( both same colour) = 1/15 + 1/15 + 1/15 = 3/15 = ⅕ or 0.2 or 20%