Question

a box has green and white thumb pins. the probability of picking a green thumb pin is 3z and probability of picking a white thumb pin is 5z. how many white thumb pins are there in the box if the total number of thumb pins is 56?

Explanation:

Step1: Find the value of \(z\)

Since the sum of probabilities of all possible outcomes is \(1\).
The probability of picking a green thumb - pin is \(3z\) and the probability of picking a white thumb - pin is \(5z\). So, \(3z + 5z=1\), which simplifies to \(8z = 1\), and then \(z=\frac{1}{8}\).

Step2: Calculate the number of white thumb - pins

The probability of picking a white thumb - pin is \(5z\). Substitute \(z = \frac{1}{8}\), the probability of picking a white thumb - pin is \(P(\text{white})=\frac{5}{8}\).
If the total number of thumb - pins \(N = 56\), and let the number of white thumb - pins be \(n\). Using the formula \(P=\frac{n}{N}\), we have \(n = P\times N\).
Substitute \(P=\frac{5}{8}\) and \(N = 56\) into the formula: \(n=\frac{5}{8}\times56\).
\(n = 5\times7=35\).

Answer:

35