Question

A professor has 24 pairs of socks in his drawer. 18 pairs are black and the rest are brown. He always wears black pants. He does not pay much attention to which socks he puts on each day. Supposed he selects one pair of socks on Monday and one on Tuesday. Since he has lots of clean socks in the drawer he does not do laundry. What is the likelihood that the professor's socks matched his pants on both days (i.e. he picked black socks)

Answer 1

Answer:

The likelihood that the professor's socks matched his pants on both days is 0.5625

Step-by-step explanation:

Total no. of pair of socks = 24

No. of black pairs = 18

We are given that  he selects one pair of socks on Monday and one on Tuesday. Since he has lots of clean socks in the drawer he does not do laundry.

So, It is  a case of replacement

He always wears black pants.

We are supposed to find he likelihood that the professor's socks matched his pants on both days i.e. Black socks both days.

So ,Probability of wearing black socks on Monday = $\frac{18}{24}$

So ,Probability of wearing black socks on Tuesday =$\frac{18}{24}$

So,the likelihood that the professor's socks matched his pants on both days = $\frac{18}{24} \times \frac{18}{24}=0.5625$

Hence the likelihood that the professor's socks matched his pants on both days is 0.5625