Answer:
Probability that the two socks picked by Natalie are of the same colours = (17/32) = 0.53125
Step-by-step explanation:
Complete Question
Natalie has 8 socks in a drawer.
5 of the socks are black.
3 of the socks are white.
Natalie takes out a sock at random, writes down its colour and puts it back into
the drawer. Then Natalie takes out a second sock, at random, and writes down its colour.
Work out the probability that the two socks are of the same colour.
Solution
This is a probability that involves replacement.
Probability of an event is given as the number of elements in the event divided by the total number of elements in the sample space.
If the event that a black socks is picked = P(B)
Then, the event that a white socks is picked = P(W)
P(B) = n(B) ÷ n(S)
n(B) = 5
n(S) = 8
P(B) = (5/8)
P(W) = n(W) ÷ n(S) = (3/8)
Probability that the two socks picked by Natalie are of the same colours = (Probability that the two socks picked are black) + (Probability that the two socks picked by Natalie are white)
Probability that the two socks picked are black = (5/8) × (5/8) (since the socks are picked and replaced, the probability stays the same)
= (25/64)
Probability that the two socks picked by Natalie are white = (3/8) × (3/8) = (9/64)
Probability that the two socks picked by Natalie are of the same colours
= (25/64) + (9/64)
= (34/64)
= (17/32) = 0.53125
Hope this Helps!!!
