A factory makes three kinds of bolts: Bolt A, Bolt B and Bolt C. It makes twice

Question

A factory makes three kinds of bolts: Bolt A, Bolt B and Bolt C. It makes twice as many of Bolt B as it doe Bolt A. The number of Bolt C made is twice the total of Bolts A and B combined. Four bolts are randoml chosen from all the bolts produced by the factory. (a) Find the probability that two of Bolt B and two of Bolt C will be chosen. (b) Find the probability that there are more Bolt B than Bolt A but no more than Bolt C (c) Find the correlation coefficient between the numbers of Bolt A and Bolt C

Explanation / Answer

Number of A bolts =n

Number of B bolts =2n

Number of C bolts =2*(n+2n) = 6n

a) Prob of exactly 2 B and 2 C bolts = (2n C 2) * (6n C 2)/ (9n C 4)

You can substitue any value of n and get the answer based upon the value of n

b) Prob C>=B>A

and C+B+A =4

i.e. there is 2 cases for the same while we pick

case 1: C=3,B=1 and A=0

Case 2: C=2,B=2 and A=0

So the ultimate prob = (2n C 1) * (6n C 3)/ (9n C 4) + (2n C 2) * (6n C 2)/ (9n C 4)

You can substitue any value of n and get the answer based upon the value of n

c) To find the correlation coefficient you need to have some values of A as well as C

and now we will take the base case of question b where we have A=1 then C=3 and A=2 then C=2

And using the correlation formula Cor (A,C) = Cov(A,C)/(sd(A)*sd(C)) = -1

which indicates that increase in the value of picking A decreses the chance of picking C linearly and so the correlation coefficient is -1 here.

Hope the above answer has helped you in understanding the proble. Please upvote the ans if it has really helped you. Good Luck!!

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.