Question

a toymaker releases a batch of new toys. 31 are wood trains, 11 are wind - up cars, 25 are action figures, and 13 are model airplanes. find the probability that a toy is not a wind - up car. p(not a wind up car) = ? round your answer to the nearest hundredth.

Explanation:

Step1: Calculate total number of toys

To find the total number of toys, we sum up the number of each type of toy. So we add 31 (wood trains), 11 (wind - up cars), 25 (action figures), and 13 (model airplanes).
The formula for the total number of toys \(N\) is \(N=31 + 11+25 + 13\).
\(31+11 = 42\), \(42+25=67\), \(67 + 13=80\). So the total number of toys \(N = 80\).

Step2: Calculate number of non - wind - up car toys

The number of wind - up cars is 11. So the number of toys that are not wind - up cars is the total number of toys minus the number of wind - up cars. Let \(n\) be the number of non - wind - up car toys. Then \(n=N - 11\).
Since \(N = 80\), \(n=80 - 11=69\).

Step3: Calculate the probability

The probability \(P(\text{Not a Wind Up Car})\) is the number of non - wind - up car toys divided by the total number of toys. The formula for probability \(P=\frac{n}{N}\).
Substituting \(n = 69\) and \(N = 80\) into the formula, we get \(P=\frac{69}{80}\).
\(\frac{69}{80}=0.8625\). Rounding to the nearest hundredth, we look at the thousandth place digit, which is 2. Since \(2<5\), we round down. So \(0.8625\approx0.86\).

Answer:

\(0.86\)