Slips of paper with the numbers one through 20 are placed in a hat. If a slip of paper is pulled out of the hat and discarded and then another slip of paper is picked find the probability of both numbers will be greater than 18 or both numbers will be less than three
there are 2 numbers greater than 18, less than three there are two.
Pr=2/20*1/19 + 2/20*1/19
Each individual letter of the word Massachusetts is placed on a piece of paper, and all 13 pieces of paper are placed in a hat. If one letter is selected at random from the hat, find the probability that a consonant is selected.
To find the probability of both numbers being greater than 18 or less than three, we need to calculate the number of favorable outcomes and the total number of possible outcomes.
Step 1: Calculate the number of favorable outcomes:
For both numbers to be greater than 18, there are two slips of paper corresponding to the numbers 19 and 20.
For both numbers to be less than three, there are two slips of paper corresponding to the numbers 1 and 2.
Therefore, there are a total of 2 favorable outcomes.
Step 2: Calculate the total number of possible outcomes:
There are 20 slips of paper in total.
After the first slip of paper is picked and discarded, there are 19 slips of paper remaining.
Therefore, there are a total of 20 * 19 = 380 possible outcomes.
Step 3: Calculate the probability:
The probability is given by the ratio of the number of favorable outcomes to the total number of possible outcomes.
Probability = Number of favorable outcomes / Total number of possible outcomes
Probability = 2 / 380
Probability = 1 / 190
Therefore, the probability is 1/190 that both numbers pulled will be greater than 18 or both numbers will be less than three.
To find the probability of both numbers being greater than 18 or both numbers being less than 3, we first need to determine the total number of possible outcomes.
There are 20 slips of paper in the hat, so the total number of possible outcomes is 20.
Now let's calculate the number of favorable outcomes for each case.
Case 1: Both numbers are greater than 18.
There are 2 slips of paper greater than 18 (19 and 20). We discarded one slip after the first pick, so there is only 1 slip remaining for the second pick.
The number of favorable outcomes for this case is 2 * 1 = 2.
Case 2: Both numbers are less than 3.
There are 2 slips of paper less than 3 (1 and 2). We discarded one slip after the first pick, so there is only 1 slip remaining for the second pick.
The number of favorable outcomes for this case is also 2 * 1 = 2.
Now we can calculate the total number of favorable outcomes by adding the favorable outcomes from each case: 2 + 2 = 4.
Finally, we can calculate the probability by dividing the number of favorable outcomes by the total number of possible outcomes:
Probability = Favorable outcomes / Total outcomes = 4 / 20 = 1/5 = 0.2 = 20%.
Therefore, the probability of both numbers being greater than 18 or both numbers being less than 3 is 20%.