In a school, four out of five students have a calculator. If 2 students are picked at random what is the probability that both have a calculator
To solve this problem, we need to find the probability of picking two students who both have a calculator out of all possible pairs of students.
Given that four out of five students have a calculator, the probability that the first student picked has a calculator is 4/5.
Since the first student is already picked, there are four students left with calculators out of the remaining four students. Therefore, the probability that the second student picked also has a calculator is 4/4 or 1.
To find the combined probability of both events happening, we multiply the probabilities together:
P(both students have a calculator) = (4/5) * (1/1) = 4/5
So the probability that both students picked have a calculator is 4/5 or 0.8.
To find the probability that both students have a calculator, we need to determine the probability of the first student having a calculator and the probability of the second student also having a calculator, given that the first student already has a calculator.
Let's break it down step-by-step:
1. Find the probability of the first student having a calculator: Since four out of five students have a calculator, the probability that the first student has a calculator is 4/5.
2. Find the probability of the second student having a calculator, given that the first student already has a calculator: Since the first student already has a calculator, we have one less student who may or may not have a calculator. So, out of the remaining four students, three have a calculator. Therefore, the probability that the second student has a calculator is 3/4.
3. Multiply the probabilities of both events occurring: To find the probability of both events happening (the first student having a calculator and the second student having a calculator, given that the first student already has one), we multiply the probabilities:
(4/5) * (3/4) = 12/20 = 3/5
Therefore, the probability that both students have a calculator is 3/5.
To find the probability that both students have a calculator, we need to determine the number of favorable outcomes (when both students have a calculator) and the total number of possible outcomes.
First, let's calculate the total number of possible outcomes. We are picking 2 students out of the entire school, so the total number of possible outcomes is given by the combination formula, denoted as "nCr", which stands for "n choose r". In this case, "n" is the total number of students in the school, and "r" is the number of students we are picking. The combination formula is:
nCr = n! / (r!(n-r)!)
In this scenario, n is the total number of students in the school, which is not mentioned in the question. Hence, we cannot determine the exact value for n.
Once we know the value of n, we can substitute it into the combination formula and calculate the total number of possible outcomes.
Now, let's consider the number of favorable outcomes. Since four out of five students have a calculator, the probability that a randomly selected student has a calculator is 4/5. When we pick two students, we need both of them to have a calculator. Therefore, the probability that both students have a calculator is the product of the probabilities for each student having a calculator:
P(both have a calculator) = (4/5) * (4/5)
Simplifying, we get:
P(both have a calculator) = 16/25
So, to find the exact probability, we need to know the total number of students in the school (n).