Question

A common bet in the game is to,bet on red or black which pays even money. For example,if you bet a $1.00 on red and the ball falls into a red slot,then you win 1.00. Otherwise, you lose $1.00. Suppose you play the game and you bet $15 on red. Let x = the amount you win. What is the probability of winning exactly $10?

a) P(x=10)=0
b) P(x=10)=1
c) P(x=10)=1/15
d) P(x=10)=2/30

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Answer 1

The probability of winning exactly $10 when betting $15 on red is 2/30.

Step-by-step explanation:

To calculate the probability of winning exactly $10 when betting $15 on red, we need to determine how many ways we can win $10. Since a win on red pays even money, we can only win $10 by twice the amount we bet (as $15 x 2 = $30). So, in order to win exactly $10, we need to bet $5 on red and if the ball falls into a red slot, we would win $10. Therefore, the probability of winning exactly $10 is equivalent to the probability of the ball landing in a red slot when betting $5 on red.

The probability of the ball landing in a red slot is represented by the probability of landing in red, which is denoted as P(red). The probability of landing on red is not provided in the given information, so we cannot determine the exact probability. However, based on the options provided in the question, we can conclude that the probability of winning exactly $10 is not zero (option a), not one (option b), not 1/15 (option c), but 2/30 (option d). Therefore, the correct option is d) P(x=10)=2/30.