Respuesta :
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 E occurring is:
[tex]P (E)=\frac{n(E)}{N}[/tex]
Here,
n (E) = favorable outcomes
N = total number of outcomes
Let X = number of defective electric toothbrushes sold.
The number of electric toothbrushes that were delivered to a store is, n = 20.
Number of defective electric toothbrushes is, x = 3.
The number of ways to select two toothbrushes to sell from the 20 toothbrushes is:
[tex]{20\choose 2}=\frac{20!}{2!(20-2)!}=\frac{20!}{2!\times 18!}=\frac{20\times 19\times 18!}{2!\times 18!}=190[/tex]
The number of ways to select two defective toothbrushes to sell from the 3 defective toothbrushes is:
[tex]{3\choose 2}=\frac{3!}{2!(3-2)!}=\frac{3!}{2!\times 1!}=3[/tex]
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
[tex]=\frac{3}{190}\\[/tex]
[tex]=0.01579\\\approx0.016[/tex]
Thus, the probability that the first two electric toothbrushes sold are defective is 0.016.
