Interview Question

Question

You have to play three games with opponents A and B in a specified sequence. You win the series if you win two consecutive games. A is a stronger player than B. Which sequence maximizes your chance of winning the series?

1. AAB
2. ABA
3. BAB
4. BAA
5. All are the same.

Comments

Hey, how this is possible? let's Understand the question first, 1. We need to win 2 matches in 3 games with the opponents A & B, 2.A is stringer than B. what is the possible sequence to win? .

now think logically, if A is stronger than B, then A is ultimately the strongest opponent to defeat, where the wining probability is low, and with the opponent B, we have the more chance to win the match. from the options, the possible sequence to win is BAB (option C) will be the right answer.

Answer 1

Option B is correct because You must win 2nd game to will series, So ABA  not other bcz  A is a stronger player than B

Answer 2

A is a stronger player than B so probability of wining A is higher then probability of wining B .

let  W=win L=lost

Probability of wining A to you = 3/4 , W= 0.75 L=0.25

Probability of wining B to you = 1/2=0.50 L=0.5

Case 1: AAB     

probability for you to win series = WWL + LWW+WWW= 0.25*0.25*0.5+0.75*0.25*0.5+0.25*0.25*0.5=0.15625

Case 2: ABA

probability for you to win series = WWL + LWW+WWW= 0.25*0.5*0.75+0.75*0.5*0.25+0.25*0.5*0.25=0.21875

Case 3: BAB

probability for you to win series = WWL + LWW+WWW=0.5*0.25*0.5+0.5*0.25*0.5+0.5*0.25*0.5=0.1875

Case 4: BAA

probability for you to win series = WWL + LWW+WWW=0.15625

so ABA sequence will maximize our chances to win seriese Ans=2

Comments

@Dharmendra Lodhi Why are we taking probability of winning A : 3/4?

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I think we can take any value. It should just be greater than 50%.

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@Dharmendra Lodhi Why WLW is not taken as case?