Question

A lottery game is set up so that each player chooses five different numbers from 1 to 50. If the five numbers chosen match the five numbers drawn randomly, the player wins (or shares) the top cash prize. With one lottery ticket, what is the probability of winning the prize? Express the answer as a fraction and as a decimal, correct to ten places.

Name: Problem 62, Chapter 11: Precalculus
Uploaded: 2021-09-12T16:54:41-08:00
Duration: 2 min 36 s
Channel: Farnood Ensan
Description: A lottery game is set up so that each player chooses five different numbers from 1 to 50. If the five numbers chosen match the five numbers drawn randomly, the player wins (or shares) the top cash prize. With one lottery ticket, what is the probability of winning the prize? Express the answer as a fraction and as a decimal, correct to ten places.

   A lottery game is set up so that each player chooses five different numbers from 1 to 50. If the five numbers chosen match the five numbers drawn randomly, the player wins (or shares) the top cash prize. With one lottery ticket, what is the probability of winning the prize? Express the answer as a fraction and as a decimal, correct to ten places.

Precalculus

Robert Blitzer 6th Edition

Chapter 11, Problem 62

Instant Answer

Solved by Expert Farnood Ensan

09/12/2021

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In this lottery game, each player chooses five different numbers from 1 to 50. If the five numbers chosen match the five numbers drawn randomly, the player wins the top cash prize. We are asked to find the probability of winning the prize with one lottery ticket. Show more…

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A lottery game is set up so that each player chooses five different numbers from 1 to 50. If the five numbers chosen match the five numbers drawn randomly, the player wins (or shares) the top cash prize. With one lottery ticket, what is the probability of winning the prize? Express the answer as a fraction and as a decimal, correct to ten places.

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Key Concepts

Combinations (Binomial Coefficient)

Combinations are used to count the number of ways to choose a subset of items from a larger set when the order of selection does not matter. The mathematical expression for combinations is C(n, k) = n! / (k!(n-k)!), where n is the total number of items and k is the number of items chosen. This concept is fundamental in determining the total number of possible lottery tickets or outcomes.

Probability

Probability quantifies the chance or likelihood that a specific event will occur, typically calculated as the ratio of the number of favorable outcomes to the total number of equally likely outcomes. In many lottery scenarios, each ticket represents a single possible outcome, and the probability of winning is found by comparing that one favorable outcome against all the possible combinations.

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