The numbers 1 to 15 are placed in a hat, and a number is selected. What is the probability that the number is 4 given it is known to be an even number?
sounds like conditional probabilty
Prog(A|B) , (read as the prob of A, given B)
= prob(A AND B)/prob(B)
prob(A and B) = 1/15
prob(B) = 7/15
prob( as stated) = (1/15) / (7/15)
= 1/7
(of course, since the 4 is one of the 7 even numbers from 1 - 15)
Ah, the wonderful world of probabilities! Let me put on my clown hat and calculate this for you.
We know that half of the numbers from 1 to 15 are even, so there are 15/2 = 7.5 even numbers. Now, since we can't pull out half of a number from the hat, let's consider that as 7 even numbers.
Out of these 7 even numbers, only one of them is 4. So, the probability of picking the number 4 from the hat, given that it is an even number, is 1 out of 7.
Therefore, the probability of randomly selecting the number 4, given that it is an even number, is 1/7.
Keep in mind, though, that these numbers might want to put on a little magic show and surprise us. Probability can be quite a tricky business sometimes!
To find the probability that the number is 4 given that it is known to be an even number, we need to determine the number of favorable outcomes and the total number of outcomes.
First, let's identify the favorable outcomes. Since it is known to be an even number, we can consider the numbers 2, 4, 6, 8, 10, 12, and 14 as favorable outcomes.
Next, let's determine the total number of outcomes. We are given that there are 15 numbers in total, from 1 to 15. Out of these, half are even numbers (2, 4, 6, 8, 10, 12, 14) and half are odd numbers (1, 3, 5, 7, 9, 11, 13, 15).
Therefore, the total number of outcomes is 15/2 = 7.5.
Finally, let's calculate the probability:
Probability = (Number of favorable outcomes) / (Total number of outcomes)
Probability = 1 (since there is only one number 4 among the favorable outcomes) / 7.5
Hence, the probability that the number is 4 given it is known to be an even number is approximately 0.1333 or 13.33%.
To determine the probability of selecting the number 4 from the hat, given that it is known to be an even number, we need to first determine the number of even numbers in the set of numbers from 1 to 15.
Step 1: Count the number of even numbers from 1 to 15.
In this case, we have 7 even numbers: 2, 4, 6, 8, 10, 12, 14.
Step 2: Determine the number of even numbers that are 4.
Since 4 is one of the even numbers, there is only one even number that is 4.
Step 3: Calculate the probability.
The probability is defined as the number of favorable outcomes divided by the number of possible outcomes. In this case, the number of favorable outcomes is 1 (the number 4) and the number of possible outcomes is 7 (the total number of even numbers).
Therefore, the probability of selecting the number 4, given that it is known to be an even number, is 1/7 or approximately 0.143 (rounded to three decimal places).