in a lottery, a player wins or shares in the jackpot by selecting the correct 6-number combination when six different numbers from 1 through 49 are drawn. if a player selects one particular 6-number combination, find the probability of winning the jackpot.
If the events are independent, the probability of both/all events occurring is determined by multiplying the probabilities of the individual events.
1/49 * 1/48 * 1/47 * 1/46 * 1/45 * 1/44 = ?
There is an equation for this, but I don't remember it.
To find the probability of winning the jackpot in a lottery, we need to determine the total number of possible outcomes and the number of favorable outcomes (winning combinations).
Step 1: Find the total number of possible outcomes:
In this case, there are 49 numbers to choose from, and we need to select 6 different numbers. We can find the total number of possible combinations using the formula for combinations: C(n, r) = n! / (r!(n-r)!), where n is the total number of items, and r is the number we want to choose.
Total number of possible combinations = C(49, 6) = 49! / (6!(49-6)!) = 13,983,816
Step 2: Find the number of favorable outcomes (winning combination):
Since the player has selected one specific 6-number combination, there is only one winning combination (favorable outcome).
Number of favorable outcomes = 1
Step 3: Calculating the probability:
Probability = Number of favorable outcomes / Total number of possible outcomes
= 1 / 13,983,816
Therefore, the probability of winning the jackpot with a specific 6-number combination is approximately 1 in 13,983,816.