a carnival has a duck pond booth. You choose a rubber duck at random,7 ducks marked as large-prize winners, 9 ducks marked as medium prize winners, and 26 ducks marked as small prize winners. What is the theoretical probability of winning a small prize at the duck pond. Express answer as a decimal.
26/(7+9+26) = ?
To find the theoretical probability of winning a small prize at the duck pond, we need to determine the ratio of the number of small prize-winning ducks to the total number of all ducks.
In this case, the number of small prize-winning ducks is 26. The total number of all ducks is the sum of the large-prize winners (7), medium prize winners (9), and small prize winners (26):
Total number of ducks = 7 + 9 + 26 = 42 ducks.
Therefore, the theoretical probability of winning a small prize is:
P(small prize) = Number of small prize-winning ducks / Total number of ducks
P(small prize) = 26 / 42
P(small prize) = 0.619
Thus, the theoretical probability of winning a small prize at the duck pond is approximately 0.619 (rounded to three decimal places).