At a large assembly line, the manufacturer reassigns employees to different task

Question

At a large assembly line, the manufacturer reassigns employees to different tasks each month. This keeps the workers from getting bored by endlessly repeating the same task. It also lets them see how the work done in different stages must fit together. It is known that 65% of the employees have less than or equal to two years of experience, 21% have between three and five years of experience, and the rest have more than five years of experience. Assume that teams of three employees are formed randomly. Dave works at this assembly line. Complete parts (a) and (b) below.

(a) Consider one of Dave's teammates. What is the probability that this teammate has 1. two or fewer years of experience? 2. more than five years of experience?

1. The probability that this teammate has two or fewer years of experience is _____. (Type an integer or a decimal.)

2. The probability that this teammate has more than five years of experience is _____. (Type an integer or a decimal.)

(b) What is the probability that, considering both of Dave's two teammates,

1. both have more than two years of experience?

2. exactly one of them has more than five years of experience?

3. at least one has more than five years of experience?

1. The probability that both of Dave's two teammates have more than two years of experience is _____. (Type an integer or a decimal.)

2. The probability that exactly one of Dave's two teammates has more than five years of experience is _____. (Type an integer or a decimal.)

3. The probability that at least one of Dave's two teammates has more than five years of experience is _____. (Type an integer or a decimal.)

Explanation / Answer

1. The probability that this teammate has two or fewer years of experience is _____. (Type an integer or a decimal.)

0.65

2. The probability that this teammate has more than five years of experience is _____. (Type an integer or a decimal.)

1-0.65-0.21=0.14

1. both have more than two years of experience?

0.65*0.65 = 0.4225

1 - 0.4225 = 0.5775

Probability = 57.75%

2. exactly one of them has more than five years of experience?

0.14

3. at least one has more than five years of experience?

0.14 + 0.14*0.14 = 0.1596

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