A box has 11 parts of which 4 are defective and 7 acceptable. 2 parts are...

A box has 11 parts of which 4 are defective and 7 acceptable. 2 parts are chosen at random without replacement. Find the probability that:

a) both parts are defective.

b) both parts are acceptable.

c) only one part is defective.

Solutions

Expert Solution

Box has 4 defective parts and 7 acceptable parts

a) Probability of picking a defective part in first pick = 4/11

Probability of picking a defective part in second pick = 3/10 since 1 defective part was already picked

Therefore probability of picking both defective parts = (4/11)*(3/10) = 6/55 = 0.1091

b) Probability of picking an acceptable part in first pick = 7/11

Probability of picking an acceptable part in second pick = 6/10 since 1 acceptable part was already picked

Therefore probability of picking both acceptable parts = (7/11)*(6/10) = 21/55 = 0.3818

c) Case 1:

Probability of picking an acceptable part in first pick = 7/11

Probability of picking a defective part in second pick = 4/10

Case 2:

Probability of picking a defective part in first pick = 4/11

Probability of picking an acceptable part in second pick = 7/10

Therefore probability of picking only one defective part = (7/11)*(4/10) +(4/11)*(7/10) = 28/55 = 0.5091

milcah answered 8 months ago

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