In a drawer there are 5 black socks and 3 green socks. Two socks are picked randomly one after the other without replacement. What is the possibility that both the socks are black?
Correct Answer: $$\frac{{5}}{{14}}$$
Number of Black socks = 5
Total socks = 5 + 3 = 8
First we draw one sock
Probability of it being black = $$\frac{{5}}{{8}}$$
Now a second sock is picked
Probability of its being black = $$\frac{{4}}{{7}}$$
Total Probability $$ = \frac{5}{8} \times \frac{4}{7} = \frac{5}{{14}}$$
Total socks = 5 + 3 = 8
First we draw one sock
Probability of it being black = $$\frac{{5}}{{8}}$$
Now a second sock is picked
Probability of its being black = $$\frac{{4}}{{7}}$$
Total Probability $$ = \frac{5}{8} \times \frac{4}{7} = \frac{5}{{14}}$$