Winning the jackpot in a lottery requires that you select the correct three numbers between 1 and 51 and in a another separate drawing you must select the correct single number between 1 and 15. Find the probability of winning the jackpot-
The probability of winning the jackpot is..?
n = 53 r = 3 (53C3)
n = 15 r = 1 (15C1)
(53C3)* (15C1)= 351,390
The probability of winning the jackpot is..? one over/ 351,390
1/351,390
To find the probability of winning the jackpot, we need to calculate the probability of correctly selecting three numbers between 1 and 51 and the probability of correctly selecting a single number between 1 and 15.
First, let's calculate the probability of correctly selecting three numbers between 1 and 51. The total number of possible number combinations is given by the formula:
Total number of combinations = nCr(51, 3)
Where nCr represents the combination formula:
nCr(n, r) = n! / (r! * (n - r)!)
For our case, n = 51 and r = 3. So, we can calculate the total number of combinations:
nCr(51, 3) = 51! / (3! * (51 - 3)!)
Next, let's calculate the probability of correctly selecting a single number between 1 and 15. Since there is only one correct number and 15 possible options, the probability is simply 1/15.
To find the probability of both events occurring (winning the jackpot), we need to multiply the probabilities of both events:
Probability of winning the jackpot = (nCr(51, 3) * 1/15)
Now, let's calculate the values:
nCr(51, 3) = 51! / (3! * (51 - 3)!)
= 51! / (3! * 48!)
= (51 * 50 * 49) / (3 * 2 * 1)
Probability of winning the jackpot = ((51 * 50 * 49) / (3 * 2 * 1)) * 1/15
Now evaluate the equation to find the probability.
If the events are independent, the probability of both/all events occurring is determined by multiplying the probabilities of the individual events.
1/51 * 1/50 * 1/49 * 1/15 = ?