# Case study Chapter 13 (Probability)

A coach is training 3 players. He observes that the player A can hit a target 4 times in 5 shots, player B can hit 3 times in 4 shots and the player C can hit 2 times in 3 shots

from this situation answer the following(Case study problem probability 6 chapter 13 class 12)

(a) Let A: the target is hit by A, B: the target is hit by B and C: The target is hit by C. Then find the probability that A, B and C all will hit

(b) Reffering to (a),what is the probability that B, C will hit and A will lose ?

(c) With reference to the events mentioned in (a), what is the probability that any two of A, B and C will hit ?

(d) What is the probability that none of them will hit the target ?

(e) What is the probability that at least one of A, B or C will hit the target ?

Solution:  P(A) = 4/5

P(B) = 3/4 and P(C) = 2/3

P(A not hitting the target) = P(A’) = 1 – 4/5 = 1/5

P(B not hitting the target) = P(B’) = 1 – 3/4 = 1/4

P(C not hitting the target) = P(C’) = 1 – 2/3 = 1/3

(a) P(The probability that A, B and C all will hit)

= P(A).P(B).P(C)

(b) P(B and C hit and A lose)

(c) P(Any two of A, B and C will hit)

=   P(A∩B∩C’) + P(A∩B’∩C) + P(A’∩B∩C)

= P(A)×P(B)×P(C’) + P(A)×P(B’)×P(C) + P(A’)×P(B)×P(C)

= 4/5×3/4×1/3 + 4/5×1/4×2/3  + 1/5×3/4×2/3

= 12/60 + 8/60 + 6/60

= 26/60 = 13/30

(d) probability that none of them will hit the target

= P(A’∩B’∩C’)

= P(A’)×P(B’)×P(C’)

= 1/5×1/4×1/3  = 1/60

(e) probability that at least one of A, B or C will hit the target

⇒ P(A∪B∪C)  = 1 – P(A’∩B’∩C’)

= 1 – 1/ 60 = 59/60

Question :  Mahindra tractors is India’s leading farm equipment manufacturer. It is the largest tractor selling factory in the world.

This factory has two machines A and B. Past recordshows that machine A produced 60% and machine B produced 40% of the output(tractors). Further 2% of the tractors produced by machine A and 1% produced by machine B were defective. All the tractors are put into one big store hall and one tractor is chosen at random.(Case study problem probability 5 chapter 13 class 12)

Based on the above information answer the following question :

(i) Find the total probability of chosen tractor ( at random) is defective.

(ii)(a) If in random choosing, chosen tractor is defective, then find the probability that the chosen tractor is produced by machine ‘A’.

(b) If in random choosing, chosen tractor is defective, then find the probability that the chosen tractor is produced by machine ‘B’

Question: Nisha and Arun appeared for first round of an competitive examination for two vacancies. The probability of Nisha’s selection is 1/6 and that of Arun’s selection is 1/4

based on the above information, answer the following question:(Case study problem probability 7 chapter 13 class 12)

(a) Find the probability that at least one of them is selected.

(b) Find the probability that both of them are selected.

(c) Find the probability that none of them is selected

(d) Find the probability that only one of them is selected.

(e) Suppose Nisha is selected by the director and told her about two posts X and Y for which posting is independent. If the probability of posting for post X is 1/6 and for post Y is 1/7, then find the probability that Nisha is selected for at least one post.

Solution : Let A  = The event that Nisha is selected

B = The event that Arun is selected

We have,