Question

Refer to the table below to find the following probabilities.

1. What is the probability of selecting an executive with more than 10 years of service?
2. What is the probability of selecting an executive who would not remain with the company, given that he or she has more than 10 years of service?
3. What is the probability of selecting an executive with more than 10 years of service or one who would not remain with the company?
4. What is the probability of selecting an executive with at least a year and up to at most 10 years of service?

	Length of Service
Loyalty	Less than 1 Year	1–5 Years	6–10 Years	More than 10 Years	Total
Would remain	10	30	5	75	120
Would not remain	25	15	10	30	80
TOTAL	35	45	15	105	200

Answer 1

1) The probability of selecting an executive with more than 10 years of service is computed here as:

= n( > 10 years of service ) / n(total frequency )

= 105/200

= 0.525

Therefore 0.525 is the required probability here.

2) Given that there is more than 10 years of service, probability of selecting an executive who would not remain with the company is computed her eas:

= 30/105

= 0.2857

Therefore 0.2857 is the required probability here.

c) P( > 10 years of service or do not remain with the company )

= n ( > 10 years or service or do not remain with the company) / Total frequency

= (80 + 75) / 200

= 155/200

= 0.775

Therefore 0.775 is the required probability here.

d) P( >= 1 year and up to at most 10 years of service )

= (45 + 15)/200

= 0.3

Therefore 0.3 is the required probability here

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