A basket contains 6 pieces of paper numbered from 1 to 6. A hat contains the letters A, B, and C. If a blindfolded person picks a number and a letter, what is the probability that the number is even and the letter is A?
p even = 3/6 = 1/2
p A = 1/3
they are independent so
1/2 * 1/3 = 1/6
To calculate the probability that the number is even and the letter is A, we need to determine the total number of possible outcomes and the number of favorable outcomes.
Total Number of Outcomes:
There are 6 possible numbers that can be chosen (1, 2, 3, 4, 5, 6) and 3 possible letters (A, B, C). Therefore, the total number of outcomes is 6 x 3 = 18.
Favorable Outcomes:
To have an even number, we need to count even numbers in our list which are 2, 4, and 6. Since we are looking for the letter A, we only have one favorable outcome: picking an even number (2, 4, or 6) and the letter A.
Therefore, the number of favorable outcomes is 1.
Probability:
The probability is calculated by dividing the number of favorable outcomes by the total number of outcomes:
Probability = Number of Favorable Outcomes / Total Number of Outcomes
Probability = 1 / 18
Simplifying this probability, we get:
Probability = 1/18 ≈ 0.0556
So, the probability that the blindfolded person picks an even number and the letter A is approximately 0.0556.
To find the probability that the number is even and the letter is A, we need to determine the total number of possible outcomes and the number of favorable outcomes.
First, let's find the total number of possible outcomes. We have 6 numbers (1 to 6) and 3 letters (A, B, C), so the total number of outcomes is the product of these two sets: 6 (numbers) multiplied by 3 (letters), which equals 18 possible outcomes.
Next, let's determine the number of favorable outcomes. We want the number to be even (2, 4, or 6) and the letter to be A.
There are 3 even numbers (2, 4, and 6) and only 1 letter A. Therefore, the number of favorable outcomes is 3 (even numbers) multiplied by 1 (letter A), which equals 3 favorable outcomes.
Now we can find the probability 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 = 3 / 18
Simplifying, we get:
Probability = 1 / 6
Therefore, the probability that the number is even and the letter is A is 1/6.