I have a bag of tiles 0-9. Without looking select a tile, record, return tile, select a second tile. What is the probability that exactly one tile will be a prime number?
You will have 2 choices
PN -- N for not prime
NP
prob = (4/9)(5/9) + (5/9)(4/9) = 40/81
looks like I forgot how to count, there are 10 tiles not 9
so
prob = (4/10)(6/10) + (6/10)(4/10) = 48/100 = 12/25
To calculate the probability of exactly one tile being a prime number, we need to consider the possible outcomes and the total number of outcomes.
First, let's determine the total number of outcomes. Since there are 10 tiles numbered from 0 to 9 in the bag, the total number of outcomes is 10.
Next, let's calculate the number of favorable outcomes where exactly one tile is a prime number. We'll consider two cases:
Case 1: Selecting a prime number first
There are four prime numbers between 0 and 9, which are 2, 3, 5, and 7. Therefore, the number of outcomes where a prime number is selected first is 4.
Case 2: Selecting a prime number second
After selecting a non-prime number first (there are six non-prime numbers), there are still four prime numbers left in the bag. Thus, the number of outcomes where a prime number is selected second is 6 * 4 = 24.
Now, let's calculate the total number of favorable outcomes by adding up the outcomes from both cases:
Total favorable outcomes = 4 + 24 = 28.
Finally, we can calculate the probability of exactly one tile being a prime number by dividing the total favorable outcomes by the total number of outcomes:
Probability = Total favorable outcomes / Total number of outcomes
Probability = 28 / 10
Probability = 2.8
Therefore, the probability that exactly one tile will be a prime number is 2.8 or 28%.