What is the probability that the selected garment is a sock?

Question

Tomas enters his darkened room and randomly selects a garment from a

chest of drawers with two drawers. One of the drawers has 6 socks and 6 T-shirts and the

another drawer has 2 socks and 3 shorts.

Answer 1

What is the probability that the selected garment is a sock?

Tomas enters his darkened room and randomly selects a garment from a chest of drawers with two drawers. One of the drawers has 6 socks and 6 T-shirts and the another drawer has 2 socks and 3 shorts.

Detailed Solution:

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Drawer 1: D1 ==> P(D1) = 1/2

Drawer 2: D2 ==> P(D2) = 1/2

Sock in Drawer 1: S1 ==> P(S1) = 6/12 = 1/2

Sock in Drawer 2: S2 ==> P(S2) = 2/5

P(S) = P((D1 and S1) or (D2 and S2))

    = P(D1)P(S1) + P(D2)P(S2)

    = (1/2)(1/2) + (1/2)(2/5) = (1/4) + (1/5) = 9/20 = 0.45

P(S) = 0.45 <== Probability that the selected garment is a sock

Answer 2

Tomas enters his darkened room and randomly selects a garment from a

chest of drawers with two drawers. One of the drawers has 6 socks and 6 T-shirts and the

another drawer has 2 socks and 3 shorts.

P(1st drawer)=1/2

P(2nd drawer)=1/2

P(A sock I 1st drawer)= 6/12=1/2

P(A sock I 2nd drawer)= 2/5

P(A sock)=P[(1st drawer and a sock) or (2nd drawer and a sock)]

=P(1st drawer)*P(A sock I 1st drawer)+P(2nd drawer)*P(A sock I 2nd drawer)

=1/2*1/2+1/2*2/5=1/4+1/5=9/20=0.45