Question

A state lottery involves the random selection of six different numbers between 1 and 30. If you select one six number combination, what is the probability that it will be the winning combination?

A. 1/720
B. 1/593,775
C. 1/427,518,000
D. 1/789,000,000

Answer 1

Option C

The probability that it will be the winning combination is:

`P = (1)/(427518000)`

Solution:

The probability is given as:

`Probability = \frac{\text{number of favorable outcomes}}{\text{total number of outcomes}}`

Given that,

A state lottery involves the random selection of six different numbers between 1 and 30

There are 30 numbers from 1 to 30

The probability that the first digit of lottery number is same as picked can be calculated as:

`P(1) = (1)/(30)`

Since, already we picked 1 digit, now total outcomes = 30 - 1 = 29

The probability that the second digit of lottery number is same as picked can be calculated as:

`P(2) = (1)/(29)`

Similarly, The probability that the all digit of lottery number is same as picked can be calculated as:

`P = P(1) * P(2) * P(3) * P(4) * P(5) * P(6)\\\\P = (1)/(30) * (1)/(29) * (1)/(28) * (1)/(27) * (1)/(26) * (1)/(25)\\\\P = (1)/(427518000)`

Thus Option C is correct