Probability Data Analysis
We are given the following probabilities:
- Probability of passing Mathematics, $P(\text{Math}) = 40\% = 0.40$
- Probability of passing Physics, $P(\text{Physics}) = 20\% = 0.20$
- Probability of passing both Mathematics and Physics, $P(\text{Math} \cap \text{Physics}) = 10\% = 0.10$
Calculating Conditional Probability
The question asks for the probability that a student passed in Physics given that they have already passed in Mathematics. This is a conditional probability problem.
The formula for conditional probability is:
$ P(A|B) = \frac{P(A \cap B)}{P(B)} $In this case, let:
- Event A = Student passed in Physics
- Event B = Student passed in Mathematics
We want to find $P(\text{Physics}|\text{Math})$.
Applying the Formula
Using the formula with the given values:
$ P(\text{Physics}|\text{Math}) = \frac{P(\text{Physics} \cap \text{Math})}{P(\text{Math})} $Substitute the known probabilities:
$ P(\text{Physics}|\text{Math}) = \frac{0.10}{0.40} $Simplify the fraction:
$ P(\text{Physics}|\text{Math}) = \frac{10}{40} = \frac{1}{4} $Thus, the probability of a randomly selected student having passed in Physics, given they passed in Mathematics, is $1/4$.
Important Questions from Probability (Notes)
- A box contains 20 black, 22 white, and 24 red socks. If a person draws socks at random one by one without looking, what is the minimum number of socks she must pick to be certain of having at least one pair of black socks?
The following bus schedule is seen at a bus stop located somewhere in between town A and town B.
Town A-00:10, then every 20 mins
Town B-00:15, then every 20 mins
If a person arrives at this bus stop at some random time, the probability that the next bus is for town B is- Some, but not all, faces of a six-faced cubical fair die are painted red (R) and the remaining green (G); and the die is thrown until red faces come up on top 4 times.
Consider the following sequences of colours listed left to right as they appear on the top.
A: GRRRR
B: GRGRRR
Which one of the following is true? - A stick of length L is broken into two pieces at random. What is the average length of the smaller piece?
- Two students are solving the same problem independently. If the probability that the first one solves the problem is $\frac{3}{5}$ and the probability that the second solves the problem is $\frac{4}{5}$, what is the probability that at least one of them solves the problem?
