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 the game?
from 1-20
number of primes is 8
number of perfect squares = 4
with no overlap
so prob(primes or perfect squares) = 12/20
= 3/5
3/5
To find the probability of winning the game, we need to determine the total number of possible outcomes and the number of favorable outcomes.
Step 1: Determine the total number of possible outcomes.
In this case, the game consists of drawing a number from 1 to 20. Therefore, there are 20 possible outcomes.
Step 2: Determine the number of favorable outcomes.
To win the game, the number drawn must be either a prime number or a perfect square. Let's calculate the number of favorable outcomes separately for prime numbers and perfect squares.
a) Prime numbers: Prime numbers between 1 and 20 are 2, 3, 5, 7, 11, 13, 17, and 19. So, there are 8 prime numbers.
b) Perfect squares: Perfect squares between 1 and 20 are 1, 4, 9, and 16. So, there are 4 perfect squares.
Adding up the favorable outcomes for prime numbers and perfect squares, we get 8 + 4 = 12 favorable outcomes.
Step 3: Calculate the probability of winning the game.
Now, we can find 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)
= 12 / 20
= 3 / 5
= 0.6
Therefore, the probability of winning the game is 0.6 or 60%.
To find the probability of winning the game, we need to determine the total number of possible outcomes and the number of favorable outcomes.
The total number of possible outcomes is the number of numbers that can be drawn from 1-20, which is 20.
Now we need to find the number of favorable outcomes. In this case, a number is favorable if it is either a prime number or a perfect square.
First, let's consider prime numbers between 1 and 20: 2, 3, 5, 7, 11, 13, 17, and 19. There are 8 prime numbers in this range.
Next, let's consider the perfect squares between 1 and 20: 1, 4, 9, 16. There are 4 perfect squares in this range.
To avoid double counting, we need to subtract the intersection between prime numbers and perfect squares, which is the number 4. (Only the number 4 is both a prime number and a perfect square.)
So, the total number of favorable outcomes is 8 + 4 - 1 = 11.
Therefore, the probability of winning the game is the number of favorable outcomes divided by the total number of possible outcomes:
Probability = Favorable Outcomes / Total Outcomes
= 11 / 20
= 0.55
So, the probability of winning the game is 0.55 or 55%.