Multiple choice

$A$ and $B$ in order draw a marble from bag containing $5$ white and $1$ red marbles with the condition that whosoever draws the red marble first, wins the game. Marble once drawn by them are not replaced into the bag. Then their respective chances of winning are

  1. $2/3$ and $1/3$
  2. $3/5$ and $2/5$
  3. $2/5$ and $3/5$
  4. $1/2$ and $1/2$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

This is a game of drawing without replacement. The probability of A winning on the first draw is 1/6. The probability of B winning on the second draw is (5/6)*(1/5) = 1/6. Since the probabilities are equal for each turn, and the game must end, the chances are 1/2 and 1/2.

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