Question

(This is not pigeonhole) My drawer has n pairs of socks, fresh from the laundry but all separated. Each sock is labeled “Left” or “Right”. If I grab socks blindly, how many trials to I need to guarantee a good pair? Please provide a step-by-step explanation.

Answer 1

Total socks = N pairs

Total number of socks = 2N

probability formula :

The probability of an event is the number of favorable outcomes divided by the total number of outcomes possible2N

P(a)= Number of favourable outcomes/ Total number of outcomes

  

Total number of left socks = N

Total number of right socks = N

Probability of getting left socks

P(L)= total number of left socks/total number of socks

= N/2N

=1/2

Probability of getting right socks

P(R)= total number of right socks/total number of socks

= N/2N

=1/2

Probability of getting one Left socks and one right socks :

(If the probability of one event doesn’t affect the other, you have an independent event. All you do is multiply the probability of one by the probability of another.)

P(L and R) =P(L) * P(R)

= 1/2 * 1/2

= 1/4

Hence 1/4 is the probability of getting one good pair