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:

$P = \frac{1}{427518000}$

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:

$P(1) = \frac{1}{30}$

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:

$P(2) = \frac{1}{29}$

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

$P = P(1) \times P(2) \times P(3) \times P(4) \times P(5) \times P(6)\\\\P = \frac{1}{30} \times \frac{1}{29} \times \frac{1}{28} \times \frac{1}{27} \times \frac{1}{26} \times \frac{1}{25}\\\\P = \frac{1}{427518000}$

Thus Option C is correct