Suppose for a class activity we have students who get blue, yellow and white pages of paper. Some of the papers have a smiley face and others don't. Use the table provided to find the probability that a randomly selected student has smiley given that the student got a white piece of paper.
To find the probability that a randomly selected student has a smiley given that the student got a white piece of paper, we need to consider only the white paper column in the table.
From the table, we can see that out of the total 20 white papers, there are 10 white papers with a smiley face and 10 white papers without a smiley face.
Therefore, the probability that a randomly selected student has a smiley given that the student got a white piece of paper is 10/20, which simplifies to 1/2.
To find the probability that a randomly selected student has a smiley given that the student got a white piece of paper, we need to use conditional probability.
Let's look at the given table:
-----------------------------------
| Color | Smiley |
-----------------------------------
| Blue | Yes |
| Blue | No |
| Yellow | Yes |
| Yellow | No |
| White | Yes |
| White | No |
-----------------------------------
We can see that out of the students who got a white piece of paper, some have a smiley face and some don't.
To find the probability, we need to calculate the number of students who got a white piece of paper and have a smiley face, and divide it by the total number of students who got a white piece of paper.
Looking at the table, we can see that there are 2 students who got a white piece of paper and have a smiley face.
The total number of students who got a white piece of paper is also 2.
Therefore, the probability that a randomly selected student has a smiley given that the student got a white piece of paper is:
Probability = (Number of students with white paper and smiley) / (Total number of students with white paper)
Probability = 2 / 2
Probability = 1
So the probability is 1, which means any student who got a white piece of paper definitely has a smiley face.
To find the probability that a randomly selected student has a smiley face given that the student got a white piece of paper, we need to use the information given in the table.
The table should contain the number of students who received each type of paper (blue, yellow, or white), as well as the number of students who received smiley faces on each type of paper.
Let's label the table with the following information:
- P(B) = number of students who received blue paper
- P(Y) = number of students who received yellow paper
- P(W) = number of students who received white paper
- P(S|B) = number of students who received a smiley face given that they received blue paper
- P(S|Y) = number of students who received a smiley face given that they received yellow paper
- P(S|W) = number of students who received a smiley face given that they received white paper
Using this notation, we want to find P(S|W), which is the probability of a student having a smiley face given that they received a white paper.
The formula to find this probability is:
P(S|W) = P(S and W) / P(W)
- P(S and W) represents the number of students who received both a smiley face and a white paper.
- P(W) represents the number of students who received a white paper.
By substituting the values from the table into this formula, we can find the probability.