A bag soccer balls contains 8 balls with black design and 7 balls with red design with no other types of soccer balls. Coach graves reaches into the bag and randomly pulls out two soccer balls.

Question

please check my answer
a) explain these events are either dependent or independent.

i think this is independent because the coach just randomly chooses the ball.

b) what is the propability both of the balls will be the ame design color?

is it 98/15.....

Answer 1

Since probability is a value between zero and 1, you should have realized immediately that your answer made no sense.

prob of 2 black balls = 8/15 * 7/14 = 56/210
prob of 2 red balls = 7/15 * 6/15 = 42/210

so the prob of either 2 black OR 2 red balls = 98/210 = 7/15

(notice that the only other possibility would have been to have a black and then a red which would be
2(8/15 / 7/14) = 8/15
and 7/15 + 8/15 = 1 )