A number is chosen at random from the integers 10 to 30 inclusive .find the probability that the number is a) a multiple of 3 b) a multiple of 5 c) prime d) a perfect square.
30/21
There are 21 integers from 10 to 30 inclusive, (count on your fingers if you think there are only 20)
multiples of 3 are 12, 15, 18, 21, 24, 27, and 30
prob(a multiple of 3) = 7/21 = 1/3
make a similar analysis for the primes from 10 to 30,
as well as the perfect squares from 10 to 30
Write an equation that is true when x is equal to −5, 4, 0 and for no other values of x.
Well, well, let's start calculating probabilities, shall we?
a) A number is divisible by 3 if its remainder when divided by 3 is zero. So, out of the integers from 10 to 30, we have 7 numbers that are multiples of 3: 12, 15, 18, 21, 24, 27, and 30. Therefore, the probability is 7/21, which can be simplified to 1/3.
b) A number is divisible by 5 if its digit ends in either 0 or 5. Out of the given range, we have 5 numbers that are multiples of 5: 10, 15, 20, 25, and 30. Therefore, the probability is 5/21.
c) Prime numbers within the given range are 11, 13, 17, 19, and 23. Hence, the probability is 5/21.
d) Perfect squares within the given range are 16 and 25. Thus, the probability is 2/21.
Hope these probabilities put a smile on your face!
To find the probability, we need to determine the number of favorable outcomes and the total number of possible outcomes.
a) Probability that the number is a multiple of 3:
For a number to be a multiple of 3, it should be divisible by 3. The numbers in the given range that are divisible by 3 are: 12, 15, 18, 21, 24, 27, and 30. So there are a total of 7 favorable outcomes.
The total number of possible outcomes in the given range is 21 (from 10 to 30).
Therefore, the probability that the number is a multiple of 3 is 7/21, which simplifies to 1/3.
b) Probability that the number is a multiple of 5:
For a number to be a multiple of 5, it should be divisible by 5. The numbers in the given range that are divisible by 5 are: 10, 15, 20, 25, and 30. So there are a total of 5 favorable outcomes.
The total number of possible outcomes in the given range is still 21.
Therefore, the probability that the number is a multiple of 5 is 5/21.
c) Probability that the number is prime:
Prime numbers are those that have only two factors: 1 and itself. To determine the prime numbers within the given range, we need to examine each number individually: 11, 13, 17, 19, 23, and 29. So there are a total of 6 favorable outcomes.
The total number of possible outcomes in the given range remains 21.
Hence, the probability that the number is prime is 6/21, which simplifies to 2/7.
d) Probability that the number is a perfect square:
Perfect squares are numbers that are the squares of whole numbers. Within the given range, the perfect squares are: 16 and 25. So there are a total of 2 favorable outcomes.
The total number of possible outcomes in the given range is still 21.
Therefore, the probability that the number is a perfect square is 2/21.