Problema Solution
What is the probability (to the nearest whole percent) of picking two white socks out of the drawer on consecutive picks when there are 12 blue socks, 6 black socks, and 14 white socks in the drawer? Assume the first sock is replaced before selecting the second sock.
Answer provided by our tutors
If events A and B are independent, then the probability of both A and B occurring is
P(A and B) = P(A) · P(B)
event A = the first picked sock is white
event B = the second picked sock is white
event A and B = both socks are white
the events are independent and have the same probability since the first sock is replaced before selecting the second sock
P(A) = P(B) = 14/(12 + 6 + 14)
P(A) = P(B) = 7/16
P(A and B) = P(A) · P(B)
P(A and B) = (7/16)(7/16)
P(A and B) = 0.191 or 19.1% or 19% to the nearest whole percent.