Question

Among 9 electrical components exactly one is known not to function properly. if 4 components are randomly selected, find the probability that at least one does not function properly.

Answer 1

Answer:

The probability is 0.44444.

Step-by-step explanation:

Among 9 electrical components exactly one is known not to function properly.

This means 8 components work properly.

If 4 components are randomly selected, the probability that at least one does not function properly is :

$\frac{8c3 \times1c1}{9c4}$

= $\frac{56}{126} =0.44444$

Answer: The probability is 0.44444.

Answer 2

Answer:

0.4444

Step-by-step explanation:

Use the following property to ease the calculation:

P(At least one)=1-P(None)

Total number of electrical components: 9

Number that does not function well :1

Number that functions well : 8

We have $^8C_4=70$ ways to to choose 4 good components from 8.

We have $^9C_4=126$ ways to choose 4 components from a total of 9.

If all function properly then none is bad, we $^1C_0=1$ way to do this.

P(At least one)=$1-\frac{^8C_4*^1C_0}{^9C_4}$

P(At least one)=$1-\frac{70*1}{126}$

P(At least one)=0.4444