Question

Use the Counting Principle to find the probability of choosing the 8 winning lottery numbers when the numbers are chosen at random from 0 to 9.

A. 1 in 100,000,000

B. 1 in 43,046,721

C. 1 in 1,000,000,000

D. 1 in 10,000,000

Answer 1

I really don’t know but I thank it is 100,000,000

Answer 2

Answer: A. 1 in 100,000,000

Explanation:

The given digits are 0, 1, 2, 3, 4, 5, 6, 7, 8, 9)

The total number of digits = 10

Now by using the counting principle, the probability of choosing one number is given by :-

`\text{P(one number)}=(1)/(10)`

Therefore, the probability of choosing 8 numbers (with replacement ) will be :

`(1)/(10)*(1)/(10)*(1)/(10)*(1)/(10)*(1)/(10)*(1)/(10)*(1)/(10)*(1)/(10)=((1)/(10))^8=(1)/(100,000,000)`