a number is chosen at random from the interger 10 to 30 inclusive what is the probability that it is a multiple of 3, a multiple of 5, prime number , perfect square
For each part, find how many numbers have the stated characteristic, then divide by 21.
e.g. multiples of 5:
these would be 10, 15, 20, 25, and 30
so prob(a multiple of 5 ) = 5/21
Do the others the same way
A number is chosen at random from the integers 10 to 30 inclusive.find the probability that number is prime
Answer
Okay
To find the probability of each event, we need to determine the total number of integers in the given range and then count the number of integers that satisfy each condition. Let's go through each event step by step:
1. Probability of being a multiple of 3:
Start by finding the number of integers in the range, which is from 10 to 30 (inclusive).
To calculate: Total number of integers = (30 - 10) + 1 = 21.
Next, we identify the multiples of 3 within this range, which are 12, 15, 18, 21, 24, 27, and 30.
Counting these multiples, we find that there are 7 integers that are multiples of 3.
Therefore, the probability of randomly selecting an integer that is a multiple of 3 is:
Probability = (Number of desired outcomes) / (Total number of outcomes) = 7 / 21 = 1/3.
2. Probability of being a multiple of 5:
Similar to the previous step, the total number of integers in the range of 10 to 30 (inclusive) is 21.
The multiples of 5 within this range are 10, 15, 20, 25, and 30.
Counting these multiples, we find that there are 5 integers that are multiples of 5.
Therefore, the probability of randomly selecting an integer that is a multiple of 5 is:
Probability = 5 / 21.
3. Probability of being a prime number:
Again, the total number of integers in the range is 21.
To find the prime numbers within this range, we need to check each integer individually. Prime numbers are numbers greater than 1 that have no divisors other than 1 and itself.
Checking the integers in the given range, we find that the prime numbers are: 11, 13, 17, 19, 23, and 29.
Counting these prime numbers, we find that there are 6 in total.
Therefore, the probability of randomly selecting an integer that is a prime number is:
Probability = 6 / 21 = 2 / 7.
4. Probability of being a perfect square:
Once again, the total number of integers in the range is 21.
To determine the perfect squares, we need to look for integers whose square root is a whole number.
Checking each integer, we find that the perfect squares in the range are: 16 and 25.
Counting these perfect squares, we find that there are 2 in total.
Therefore, the probability of randomly selecting an integer that is a perfect square is:
Probability = 2 / 21.
In summary, the probabilities are:
- Probability of being a multiple of 3: 1/3
- Probability of being a multiple of 5: 5/21
- Probability of being a prime number: 2/7
- Probability of being a perfect square: 2/21