Message Expanded: Read Probability Posted By Terence Yi M

Message Expandedmessage Readprobabilityposted Byterence Yi Mar 26 2

Class, If you play California Super Lotto, you pick five numbers from 1 to 47 and one mega number from 1 to 27. If you buy one ticket ($1.00), what is the probability of winning the Jackpot? You must show your work.

Paper For Above instruction

The probability of winning the California Super Lotto jackpot involves calculating the likelihood of selecting the exact winning combination of numbers. The game requires players to choose five distinct numbers from 1 to 47 and one additional mega number from 1 to 27. To determine the probability of winning, we need to calculate the total number of possible combinations and then find the reciprocal of this total, since only one combination results in a jackpot win.

First, we calculate the number of ways to choose five numbers from a set of 47. Since the order in which the numbers are selected does not matter, we use the combination formula, which is given by:

C(n, k) = n! / (k! * (n - k)!)

where n is the total number of options, and k is the number of selections.

Applying this formula, the number of ways to select five numbers from 47 is:

C(47, 5) = 47! / (5! * (47 - 5)!)

Calculating this:

C(47, 5) = (47 × 46 × 45 × 44 × 43) / (5 × 4 × 3 × 2 × 1) = (1,532,028,240) / 120 = 12,869,685

Therefore, there are 12,869,685 possible combinations for choosing five numbers out of 47.

Next, the Mega number is selected independently from numbers 1 to 27, and only one specific number will match the winning number. The number of ways to choose this mega number is:

C(27, 1) = 27

Given that each of these choices is independent, the total number of possible ticket combinations is the product of the two:

Total combinations = C(47, 5) × 27 = 12,869,685 × 27 = 347,922,195

Since only one specific combination will be the winning one, the probability of selecting the winning combination with a single ticket purchase is:

Probability = 1 / Total combinations = 1 / 347,922,195 ≈ 2.876 × 10-9

This probability indicates that the chance of winning the jackpot with one ticket is approximately 2.876 in a billion, making it highly unlikely.

In conclusion, understanding the probability of winning the California Super Lotto involves calculating the total possible combinations of choosing five numbers from 47 and assembling them with a single mega number from 27. The probability, approximately 2.876 × 10-9, underscores the game's odds and the low likelihood of winning with one ticket.

References

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