In a group of friends, 50% are engineers, 35% are cricketers and 40% are married. the percentage of friends who are engineers as well as cricketers but not married is equal to the percentage of friends who are both engineers and cricketers as well as married. also, the number of married cricketers who are not engineers is equal to the number of married engineers who are not cricketers. the percentage of friends who are married, but are neither cricketers nor engineers, is 25%. q. what is the percentage of friends who are both cricketers and engineers as well as married? ?

Percentage of friends who are both cricketers and engineers as well as married = 5 %

Step-by-step explanation:

Let us assume that there are 100 friends in total.

n(E U C U M) = 100

( It is assumed that there are no members who are not engineers, not cricketers , not married)

Let E denote Engineers

C denote Cricketers

M denote Married

n(E) = 50 ; n(C) = 35 ;  n(M) = 40 ;

Friends who are engineers as well as cricketers but not married is equal to the percentage of friends who are both engineers and cricketers as well as married.

So, n(E ∩ C) = E and C but not M +  n(E ∩ C ∩ M)

Let  n(E ∩ C ∩ M) = x

So,  n(E ∩ C) = 2x

Married cricketers who are not engineers is equal to the number of married engineers who are not cricketers.

Let Married cricketers who are not engineers be 'y'.

E and M but not C = C and M but not E = y

Friends who are married, but are neither cricketers nor engineers = 25

n(M) = n( M and not E and not C) + x + 2y

40 = 25 + x + 2y

y = (15 - x) / 2

We know that the Venn diagram formula is:

n(E U C U M) = n(E) + n(C) + n(M) - n(E ∩ C) - n(E ∩ M) - n(C ∩ M)  + n(E ∩ C ∩ M)

100 = 50 + 35 + 40 - 2x - (x+y) - (x+y) + x

100  = 125 - 3x - 2y

3x + 2 / 2 * (15 - x) = 25

2 x = 10

x = 5

So, percentage of friends who are both cricketers and engineers as well as married = n(E ∩ C ∩ M) = 5 %

according to the question,engineers find a new metal that is stronger than steel but much lighter. material is also significantly cheaper than what is currently used for most aircraft, available in large quantities, and easy to manufacture. the engineers are excited because new material will lower the costs of buying and operating airplanes for companies.

in situation the safety tests should be performed before any kind of marketing or manufacturing, because safety parameters are the most necessary step to choose a new substance for building aeroplanes.

that's why option b is the most suitable answer.

Engineers - What They Do. Engineers apply the principles of science and mathematics to develop economical solutions to technical problems. Their work is the link between scientific discoveries and the commercial applications that meet societal and consumer needs. Many engineers develop new products.

Explanation:

a) The population size would be the sum of all engineers in the three groups.

Population size = 24 + 60 +36

Population size = 120

b) Here quota sampling method is used where every group has a quota of 1/4th of its population

c) The advantages of quota sampling is that it is easier to conduct and manage. It takes less time to sample as the people are already subdivided

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Explanation:

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