There are 3 economists, 4 engineers, 2 statisticians and I actuary. A committee of 4 from
among them is to be formed. Find the probability that the committee (1) consists of one
professional of each kind; (ii) has at least one economist; (iii) has the actuary as a member and
three others; (iv) has at least one engineer but no economist.
Answers
Different probabilities of Forming a committe of Economist , Engineers , statisticians and Actuary calculated
Step-by-step explanation:
There are 3 economists, 4 engineers, 2 statisticians and I actuary.
Total 10
A committee of 10 can be formed in ¹⁰C₄ ways
= 210 Ways
consists of one professional of each = 3 * 4 * 2 * 1 = 24 Ways
Probability = 24/210 = 4/35
(ii) has at least one economist;
1 economist , 2 economist , 3 economist
1 economist =³C₁ * ⁷C₃ = 105
2 economist = ³C₂ * ⁷C₂ = 63
3 economist = ³C₃ * ⁷C₁ = 7
= 175
Probability = 175/210 = 5/6
(iii) has the actuary as a member and three others = 1 * ⁹C₃ = 84 ways
Probability = 84/210 = 14/35
(iv) has at least one engineer but no economist.
if no economist then total possibilities = ⁷C₄ = 35
if no engineer also then ⁴C₀ * ³C₄ ( not possible)
so all 35 cases will have atleast 1 engineer if no economist
Probability = 35/210 = 1/6
Answer:
1/6
Step-by-step explanation:
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