A box contains 5 black and 2 white balls. 2 balls are drawn without replacement. Find the probabilit

A box contains 5 black and 2 white balls. 2 balls are drawn without replacement. Find the probability of drawing 2 black balls.


First draw probability of black is:
Total Balls in box = Black balls + white balls
Total Balls in Box = 5 + 2
Total Balls in Box = 7

P(Black) = Black Balls / Total balls in box
P(Black) = 5/7

Second draw probability of black (with no replacement) is:
Total Balls in box = Black balls + white balls
Total Balls in Box = 4 + 2
Total Balls in Box = 6

P(Black) = Black Balls / Total balls in box
P(Black) = 4/6
Using our fraction simplifier, we see that 4/6 is:
2/3

Since each event is independent, we can multiply them to find the probability of drawing 2 black balls:
P(Black, Black) = 5/7 * 2/3
P(Black, Black) = 10/21