Question

1. A student majoring in economics is looking for a job. Given his work experience and grades, the probability of getting a job offer from a firm to which he applies is 50%. If he applies to 3 firms, what is the probability that he gets 2 job offers? (Find the nearest answer.)

   	a.	24.3%
   	b.	38.4%
   	c.	43.2%
   	d.	37.5%
   	e.	44.1%

Answer 1

Let the three firms be namely A,B and C.

As given for each firm getting selected probability is 50% = 0.5

So,

Probability of getting selected by A = P(A) = 0.5

Probability of getting rejected by A = P(A') = 1 - P(A) = 1-0.5 = 0.5

Similarly,

P(B) = 0.5 and P(B') = 0.5

P(C) = 0.5 and P(C') = 0.5

Now,

Getting selected by two firms will be possible in three ways :-

1. When selected by A and B but rejected by C
2. When selected by A and C but rejected by B
3. When selected by B and C but rejected by A.

So calculating probability for each of the above three cases and then summing them will give the total probability of being selected by 2 firms.

1. Probability of being selected by A and B and rejected by C :-

P(A)*P(B)*P(C') = 0.5*0.5*0.5 = 0.125

2. Probability of being selected by A and C and rejected by B :-

P(A)*P(C)*P(B') = 0.5*0.5*0.5 = 0.125

3. Probability of being selected by B and C and rejected by A :-

P(B)*P(C)*P(A') = 0.5*0.5*0.5 = 0.125

So,

Total = 0.125 + 0.125 + 0.125

= 0.375

= 37.5%

Hence, Probability of being selected by two firms is 37.5%

So, Option d. 37.5% ​​​​​​​is correct