Answer:
The probability that the first two electric toothbrushes sold are defective is 0.016.
Step-by-step explanation:
The probability of an event, say <em>E </em>occurring is:
![P (E)=\frac{n(E)}{N}](https://tex.z-dn.net/?f=P%20%28E%29%3D%5Cfrac%7Bn%28E%29%7D%7BN%7D)
Here,
n (E) = favorable outcomes
N = total number of outcomes
Let <em>X</em> = number of defective electric toothbrushes sold.
The number of electric toothbrushes that were delivered to a store is, <em>n</em> = 20.
Number of defective electric toothbrushes is, <em>x</em> = 3.
The number of ways to select two toothbrushes to sell from the 20 toothbrushes is:
![{20\choose 2}=\frac{20!}{2!(20-2)!}=\frac{20!}{2!\times 18!}=\frac{20\times 19\times 18!}{2!\times 18!}=190](https://tex.z-dn.net/?f=%7B20%5Cchoose%202%7D%3D%5Cfrac%7B20%21%7D%7B2%21%2820-2%29%21%7D%3D%5Cfrac%7B20%21%7D%7B2%21%5Ctimes%2018%21%7D%3D%5Cfrac%7B20%5Ctimes%2019%5Ctimes%2018%21%7D%7B2%21%5Ctimes%2018%21%7D%3D190)
The number of ways to select two defective toothbrushes to sell from the 3 defective toothbrushes is:
![{3\choose 2}=\frac{3!}{2!(3-2)!}=\frac{3!}{2!\times 1!}=3](https://tex.z-dn.net/?f=%7B3%5Cchoose%202%7D%3D%5Cfrac%7B3%21%7D%7B2%21%283-2%29%21%7D%3D%5Cfrac%7B3%21%7D%7B2%21%5Ctimes%201%21%7D%3D3)
Compute the probability that the first two electric toothbrushes sold are defective as follows:
P (Selling 2 defective toothbrushes) = Favorable outcomes ÷ Total no. of outcomes
![=\frac{3}{190}\\](https://tex.z-dn.net/?f=%3D%5Cfrac%7B3%7D%7B190%7D%5C%5C)
![=0.01579\\\approx0.016](https://tex.z-dn.net/?f=%3D0.01579%5C%5C%5Capprox0.016)
Thus, the probability that the first two electric toothbrushes sold are defective is 0.016.