A game consists of drawing a number from 1□20 a player wins if the number drawn is either a prime number or a perfect square what is the probability of winning this game
20 numbers
primes
1, 3, 5, 7, 13, 17, 19 or 7 of those
squares
1 4 9 16 or 4 of them but 1 is repeated
so
7 + 3 = 10
10/20 = 1/2
Ah, the probability of winning this game? Well, let's calculate it while having a bit of fun!
First, we need to determine the total number of possibilities. Since we draw a number from 1□20, there are 20 possible outcomes.
Now, let's figure out the number of favorable outcomes, or in other words, the numbers that would make you win the game. We have two categories: prime numbers and perfect squares.
There are a total of 8 prime numbers between 1 and 20. (2, 3, 5, 7, 11, 13, 17, 19). So that gives us 8 possible favorable outcomes.
When it comes to perfect squares, we have 4 of them between 1 and 20. (1, 4, 9, 16). So that adds another 4 favorable outcomes.
Now we just add up the favorable outcomes: 8 + 4 = 12.
So, out of the 20 possible outcomes, you have 12 favorable outcomes. To calculate the probability of winning, we divide the number of favorable outcomes (12) by the total number of outcomes (20): 12/20 = 0.6.
Therefore, the probability of winning this game is 0.6 or 60%.
Just remember, even if you don't win, I guarantee I can put a smile on your face!
To find the probability of winning the game, we first need to calculate the total number of possible outcomes.
Since the game involves drawing a number from 1 to 20, there are a total of 20 possible outcomes.
Next, we need to determine the number of favorable outcomes, which are the numbers that are either prime or perfect squares.
Prime numbers from 1 to 20: 2, 3, 5, 7, 11, 13, 17, 19 (total of 8 prime numbers).
Perfect squares from 1 to 20: 1, 4, 9, 16 (total of 4 perfect squares).
To avoid double counting, we need to subtract the common number 1 since it is both a prime number and a perfect square.
Therefore, the number of favorable outcomes is 8 + 4 - 1 = 11.
Now, we can calculate the probability of winning the game by dividing the number of favorable outcomes by the total number of possible outcomes:
Probability of winning = Number of favorable outcomes / Total number of possible outcomes
= 11 / 20
= 0.55
So, the probability of winning this game is 0.55 or 55%.
To solve this problem, we need to first determine the total number of outcomes and then calculate the number of favorable outcomes.
1. Total number of outcomes:
Since the game involves drawing a number from 1 to 20, the total number of outcomes is 20 (since there are 20 possible numbers).
2. Number of favorable outcomes:
We need to find the prime numbers and perfect squares between 1 and 20.
Prime numbers less than or equal to 20: 2, 3, 5, 7, 11, 13, 17, 19 (a total of 8 numbers).
Perfect squares less than or equal to 20: 1, 4, 9, 16 (a total of 4 numbers).
3. Probability of winning the game:
The probability of winning is calculated by dividing the number of favorable outcomes by the total number of outcomes.
Probability of winning = Number of favorable outcomes / Total number of outcomes
In this case, the number of favorable outcomes is 8 (prime numbers) + 4 (perfect squares) = 12.
Probability of winning = 12 / 20 = 0.6
Therefore, the probability of winning this game is 0.6 or 60%.