Please help me out with this
The numbers 1 through 50 are written with red marker on slips of paper while the numbers 51 through 100 are written with blue marker on slips of paper. All the papers are put into a bag and shuffled. One card is randomly selected.
a. Find the probability of selecting a number less than 10 or a number written in blue. Show work.
b. Find the probability of selecting a number written in red or a multiple of 20. Show work.
P(<10 | blue) = P(<10) + P(blue) - P(<10 & blue)
= 9/100 + 50/100 - 5/100 = 54/100
similarly for (b)
ok thank you so much for showing me how to solve this!!! :)
a. To find the probability of selecting a number less than 10 or a number written in blue, we need to find the number of desired outcomes and the total number of possible outcomes.
1. Desired outcomes:
- Numbers less than 10: There are 9 numbers less than 10 (1, 2, 3, 4, 5, 6, 7, 8, and 9) written in red.
- Numbers written in blue: There are 50 numbers written in blue (51, 52, 53, ..., 99, 100).
To calculate the total number of desired outcomes, we add the numbers less than 10 and the numbers written in blue: 9 + 50 = 59.
2. Total number of possible outcomes:
The total number of slips of paper in the bag is 100 (numbers from 1 to 100), so there are 100 possible outcomes.
3. Probability:
The probability is calculated by dividing the number of desired outcomes by the total number of possible outcomes.
Probability = Number of desired outcomes / Total number of possible outcomes
Probability = 59 / 100
Probability = 0.59 or 59%
Therefore, the probability of selecting a number less than 10 or a number written in blue is 0.59 or 59%.
b. To find the probability of selecting a number written in red or a multiple of 20, we again need to determine the number of desired outcomes and the total number of possible outcomes.
1. Desired outcomes:
- Numbers written in red: There are 50 numbers (1, 2, 3, ..., 50) written in red.
- Multiples of 20: There are 5 multiples of 20 (20, 40, 60, 80, and 100).
To calculate the total number of desired outcomes, we add the numbers written in red and the multiples of 20: 50 + 5 = 55.
2. Total number of possible outcomes:
The total number of slips of paper in the bag is still 100, so there are 100 possible outcomes.
3. Probability:
The probability is again calculated by dividing the number of desired outcomes by the total number of possible outcomes.
Probability = Number of desired outcomes / Total number of possible outcomes
Probability = 55 / 100
Probability = 0.55 or 55%
Therefore, the probability of selecting a number written in red or a multiple of 20 is 0.55 or 55%.