Question

Players S₁, S₂ ..... S₁₆ are drawn into pairs at random. Matches are played between players of each pair and 8 winners are obtained. Assuming that all players are equally strong and no match is drawn. Then the probability that S₁ is among the winners

• A. ½
• B. 1/3
• C. ¼
• D. 2/3

Answer 1

Answer: (A)

½

Answer 2

n(E₁) = ¹⁵C₇

P(E₁) = $\frac { { } ^ { 15 } \mathrm { C } _ { 7 } } { { } ^ { 16 } \mathrm { C } _ { 8 } } = \frac { { } ^ { 15 } \mathrm { C } _ { 7 } } { \frac { 16 } { 8 } { } ^ { 15 } \mathrm { C } _ { 7 } } = \frac { 8 } { 16 } = \frac { 1 } { 2 }$ .