In a class of 60 students, 30 offer physics and 40 offer chemistry. If a student is picked at random from the class, what is the probability that the student offer both physics and chemistry
30+40-x = 60
find x
your probability is x/60
Well, it seems like these students are quite the multitaskers!
To find the probability of a student offering both physics and chemistry, we need to find the intersection of the two subjects.
Since there are 30 students who offer physics and 40 students who offer chemistry, we know that the maximum number of students who could offer both is 30 (because that's how many are in the physics group).
Therefore, the probability of a student offering both physics and chemistry is 30 divided by the total number of students in the class, which is 60.
So, the probability is 30/60, which simplifies to 1/2.
In other words, there's a 50% chance that the student selected offers both physics and chemistry. It's like winning a coin toss – heads, they offer both; tails, they don't!
To find the probability that a student offers both physics and chemistry, we need to determine the number of students who offer both subjects.
Let's denote the number of students who offer both physics and chemistry as "x."
Given that there are 60 students in total, we can use the principle of inclusion-exclusion to find the value of "x."
According to the principle, the total number of students offering both subjects is equal to the sum of the number of students offering physics and the number of students offering chemistry, minus the number of students offering both subjects.
In equation form: x = (number of students offering physics) + (number of students offering chemistry) - (number of students offering both)
We know that 30 students offer physics and 40 students offer chemistry. Since there are only 60 students in total, we can rewrite the equation as: x = 30 + 40 - 60.
Simplifying this equation, we get x = 10.
Therefore, 10 students offer both physics and chemistry.
To find the probability, we divide the number of students offering both subjects (10) by the total number of students (60):
Probability = Number of students offering both subjects / Total number of students
Probability = 10 / 60
Thus, the probability that a student chosen at random from the class offers both physics and chemistry is 1/6 or approximately 0.1667.
To find the probability that a student offers both physics and chemistry, we need to find the number of students who offer both subjects and divide it by the total number of students in the class.
To find the number of students who offer both physics and chemistry, we can use the principle of inclusion-exclusion. According to the principle, the number of students who offer both subjects is equal to the sum of the number of students who offer physics plus the number of students who offer chemistry, minus the number of students who offer both subjects.
Let's calculate the number of students who offer both subjects:
Number of students who offer physics = 30
Number of students who offer chemistry = 40
Number of students who offer both physics and chemistry = ?
To find the number of students who offer both physics and chemistry, we add the number of students who offer physics and the number of students who offer chemistry, and then subtract the total number of students in the class:
Number of students who offer both physics and chemistry = Number of students who offer physics + Number of students who offer chemistry - Total number of students in the class
Number of students who offer both physics and chemistry = 30 + 40 - 60
Number of students who offer both physics and chemistry = 70 - 60
Number of students who offer both physics and chemistry = 10
Now that we have the number of students who offer both physics and chemistry, we can calculate the probability:
Probability = Number of students who offer both physics and chemistry / Total number of students in the class
Probability = 10 / 60
Probability = 1 / 6
Therefore, the probability that a student offers both physics and chemistry is 1/6.