How can i solve this question with Geometric distribution or random variables?I tried have tried using a 'Geometric distribution', but it hasn't worked.John and Ron play basketball 10 times. The probability that John wins in single round = 0.4. The probability that Ron wins in single round = 0.3. The probability that there is equality between them in a single round = 0.3. The "Winner" is defined to be the first to win a single round.The rotations are different and independent.What is the probability that John is the Winner?

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How can i solve this question with Geometric distribution or random variables?I tried have tried using a &#039;Geometric distribution&#039;, but it hasn&#039;t worked.John and Ron play basketball 10 times. The probability that John wins in single round   =  0.4. The probability that Ron wins in single round   =  0.3. The probability that there is equality between them in a single round   =  0.3. The &quot;Winner&quot; is defined to be the first to win a single round.The rotations are different and independent.What is the probability that John is the Winner?

Rihanna Blanchard · Accepted Answer

Step 1Given that there are exactly 10 rounds, the probability of having no winner by the end of the 10 rounds is 0.310. Then we know that the probability of having a winner is   1  −      0.3          10      .Step 2Such probability should be apportioned between John and Ron in the ratio 0.4/0.3. So the probability that John wins is       4    7    (  1  −      0.3          10        )

ohgodamnitw0 · Accepted Answer

Explanation:Since they only play 10 times, the probability that John wins is equal to the sum of probabilities that John wins in the i-th round:  P  =      ∑          i      =      1              10            (          0.3              i        −        1              ×    0.4    )    =  0.4  ×            1      −              0.3                  10                      0.7   where the probability that John wins in the i-th round is       0.3          i      −      1        ×  0.4 because the first   i  −  1 rounds were all draws.

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