Option C
The probability that it will be the winning combination is:
[tex]P = \frac{1}{427518000}[/tex]
Solution:
The probability is given as:
[tex]Probability = \frac{\text{number of favorable outcomes}}{\text{total number of outcomes}}[/tex]
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:
[tex]P(1) = \frac{1}{30}[/tex]
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:
[tex]P(2) = \frac{1}{29}[/tex]
Similarly, The probability that the all digit of lottery number is same as picked can be calculated as:
[tex]P = P(1) \times P(2) \times P(3) \times P(4) \times P(5) \times P(6)\\\\P = \frac{1}{30} \times \frac{1}{29} \times \frac{1}{28} \times \frac{1}{27} \times \frac{1}{26} \times \frac{1}{25}\\\\P = \frac{1}{427518000}[/tex]
Thus Option C is correct
