In a game of Archery, each ring of the Archery target is valued. The centremost ring is worth 10 points and rest of the rings are allotted points 9 to 1 in sequential order moving outwards.
Archer A is likely to earn 10 points with a probability of 0·8 and Archer B is likely the earn 10 points with a probability of 0·9.
Based on the above information, answer the following questions:
If both of them hit the Archery target, then find the probability that
(a) exactly one of them earns 10 points.
(b) both of them earn 10 points.

Question

In a game of Archery, each ring of the Archery target is valued. The centremost ring is worth 10 points and rest of the rings are allotted points 9 to 1 in sequential order moving outwards.
Archer A is likely to earn 10 points with a probability of 0·8 and Archer B is likely the earn 10 points with a probability of 0·9.
Based on the above information, answer the following questions:
If both of them hit the Archery target, then find the probability that
(a) exactly one of them earns 10 points.
(b) both of them earn 10 points.

Infinity Learn · Accepted Answer

Assume, thatP(A)= probability of Archer A is likely to earn 10 points=0.8P(B)= probability of Archer B is likely to earn 10 points=0.9Now, for P’(A)=1-P(A)=1-0.8=0.2 and P’(B)=1-P(B)=1-0.9=0.1(a) Now, the required probability for exactly one of them earns 10 points=P(A)⋅P’(B)+P’(A)⋅P(B)=0.8⋅0.1+0.2⋅0.9=0.08+0.18=0.26(b) Now, the required probability for both of them earn 10 points,∴𝑃(𝐴∩𝐵)=𝑃(𝐴)×𝑃(𝐵)=0.8×0.9=0.72Therefore, (a) Required probability is 0.26,(b) Required probability is 0.72

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