Algebra

Probability

Medium

core

In a college, 30% students fail in physics, 25% fail in Mathematics and 10% fail in both. One student is chosen at random. The probability that she fails in physics if she has failed in mathematics is

2/5

1/5

9/10

3/10

✅ Correct Option: 1

Given information:

30% students fail in Physics
25% students fail in Mathematics
10% students fail in both subjects

The question asks for the probability that a student fails in Physics given that she has failed in Mathematics. This is a conditional probability problem.

Consider 100 students in the college.

Number of students who failed Mathematics = 25% of 100 = 25 students

Number of students who failed both Physics and Mathematics = 10% of 100 = 10 students

Among the 25 students who failed Mathematics, 10 students also failed Physics.

Probability that she fails in Physics given she has failed in Mathematics:

$P(\text{Physics | Mathematics}) = \dfrac{\text{Students who failed both}}{\text{Students who failed Mathematics}}$

$P(\text{Physics | Mathematics}) = \dfrac{10}{25}$

$P(\text{Physics | Mathematics}) = \dfrac{2}{5}$

Using the conditional probability formula:

$P(\text{Physics | Mathematics}) = \dfrac{P(\text{Both fail})}{P(\text{Mathematics fail})}$

$P(\text{Physics | Mathematics}) = \dfrac{0.10}{0.25}$

$P(\text{Physics | Mathematics}) = \dfrac{2}{5}$

Therefore, the probability is $\dfrac{2}{5}$ .

2022: 10 Aug Shift 1

The probability distribution of a random variable $X$ is

x	0	1	2	3
P(X = x)	$\frac{1}{4}$	$\frac{1}{8}$	$\frac{1}{8}$	$\frac{1}{2}$

The variance of $X$ is

2026: 22 May Shift 2

Two numbers are selected at random from the integers 1 through 19. If the sum is even, then the probability that both are odd numbers is:

2024: 16 May Shift 1

Two dice are thrown simultaneously. If X denotes the number of fours, then the expectation of X will be :

2025: 26 May Shift 2

Which of the following are the properties of Normal Distribution function f(x) and Normal probability curve:

(A) The probability of success remains the same in each trial and the number of trials is small in number.

(B) The curve is bell-shaped and is symmetrical about the mean.

(C) If set of n trials are repeated N times, then frequency f(r) of r successes is given by f(r) = N.p(r) = N $e^{-m\frac{m^r}{r!}}$ , r=0,1,2,...

(D) As x increases numerically, f(x) decreases rapidly and the maximum value of f(x) occurs at x=μ(mean)

Choose the correct answer from the options given below:

2026: 31 May Shift 2

The probability distribution table of a random variable X is given below.

$X_i$	$P(X_i)$
0	1/8
1	a
2	b
3	1/8

If $E(X) = \dfrac{3}{2}$ , then the values of a and b are:

2025: 19 May Shift 1

The standard deviation of the number of tails in three tosses of a coin is:

In a college, 30% students fail in physics, 25% fail in Mathematics and 10% fail in both. One student is chosen at random. The probability that she fails in physics if she has failed in mathematics is

Solution

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