Question

5. Suppose your top drawer contains different colored socks: 8 are white, 14 are black, 4 are pink, and 12 are blue. All socks in the drawer are loose (unpaired). In the morning, you randomly select two socks, one at a time. Calculate the following probabilities, writing your answer either as a decimal or a fraction.(a) What is the probability that you get a blue pair of socks? (b) What is the probability that you do not get a blue pair of socks? (c) What is the probability that you get either a white pair or a blue pair of socks? (d) What is the probability that you get one black sock and one white sock?

Answer 1

a) Probability of getting a blue pair of socks = (66/703) = 0.0939

b) Probability of not getting a blue pair of socks = (637/703) = 0.9061

c) Probability of getting either a white pair or a blue pair of socks = (94/703) = 0.1337

d) Probability of one black sock and one white sock = (112/703) = 0.1593

Step-by-step explanation

The probability of an event is calculated as the number of elements in the event divided by the number of elements in the sample space

Number of elements in the sample space

= Total number of socks

= 8 + 14 + 4 + 12

= 38

8 white socks

14 black socks

4 pink socks

12 blue socks

a) Probability of getting a blue pair of socks

= (12/38) × (11/37)

= (66/703)

= 0.0939

b) Probability of not getting a blue pair of socks

= 1 - (Probability of getting a blue pair of socks)

= 1 - (66/703)

= (637/703)

= 0.9061

c) Probability of getting either a white pair or a blue pair of socks

= (Probability of getting a white pair of socks) + (Probability of getting a blue pair of socks)

= [(8/38) ×(7/37)] + (66/703)

= (28/703) + (66/703)

= (94/703)

= 0.1337

d) Probability of one black sock and one white sock

= (Probability of getting a black sock first, then a white sock) + (Probability of getting a white sock first, then a black sock)

= [(14/38) × (8/37)] + [(8/38) + (14/37)]

= (56/703) + (56/703)

= (112/703)

= 0.1593

Hope this Helps!!!