Question

A carnival has a duck pond booth. You choose a rubber duck at random. The mark on the bottom of the duck tells you whether you won a small, medium, or large prize, or no prize at all. There are 65 ducks floating in the pond. There are 3 marked as large-prize winners, 13 ducks marked as medium-prize winners, and 21 ducks marked as small-prize winners. Find the theoretical probability of winning a medium prize at the duck pond. Express your answer as a decimal. If necessary, round your answer to the nearest thousandth.
21/65
1/21
1/12
1/5

Answer 1

Answer: the theoretical probability of winning a medium prize at the duck pond= 1/5 or 0.2.

Step-by-step explanation:

Given: The total number of ducks in the pond =65

The number of ducks marked as medium-prize winners=13

Now, the probability of of winning a medium prize at the duck pond is given by:-

$P(M)=\frac{\text{ducks marked as medium-prize winners}}{\text{total ducks}}\\\\\Rightarrow\ P(M)=\frac{13}{65}\\\\\Rightarrow\ P(M)=\frac{1}{5}\\\Rightarrow\ P(M)=0.2$

Hence,  the theoretical probability of winning a medium prize at the duck pond= 1/5 or 0.2.