a number is picked from the set {1,2,3,-,18}.find the probability that it is either a multiple of 3 or a number less than 7
Maths
"...either a multiple of 3 or a number less than 7"
only 2 elements satisfy that condition, namely the 3 and 6
so prob(of your event) = 2/18 = 1/9
To find the probability that a number picked from the set {1, 2, 3, ..., 18} is either a multiple of 3 or a number less than 7, we need to determine the number of favorable outcomes and the total number of possible outcomes.
Step 1: Determine the number of favorable outcomes.
In this case, the favorable outcomes are the numbers that are either a multiple of 3 or less than 7.
Multiples of 3 in the set: {3, 6, 9, 12, 15, 18} (total of 6 numbers)
Numbers less than 7 in the set: {1, 2, 3, 4, 5, 6} (total of 6 numbers)
However, we need to be careful not to count the number 3 twice since it satisfies both conditions (multiple of 3 and less than 7). Therefore, we remove one occurrence of 3 from the count.
Total number of favorable outcomes = 6 + 6 - 1 = 11
Step 2: Determine the total number of possible outcomes.
The total number of elements in the set is 18.
Total number of possible outcomes = 18
Step 3: Calculate the probability.
The probability is calculated by dividing the number of favorable outcomes by the total number of possible outcomes.
Probability = Number of favorable outcomes / Total number of possible outcomes
Probability = 11 / 18
Therefore, the probability that a number picked from the set {1, 2, 3, ..., 18} is either a multiple of 3 or a number less than 7 is 11/18.