Let \( E \) and \( F \) be two events such that \( P(E) = 0.1 \), \( P(F) = 0.3 \), \( P(E \cup F) = 0.4 \). Then \( P(F|E) \) is:
Show Hint
- \( 0.6 \)
- \( 0.4 \)
- \( 0.5 \)
- \( 0 \)
The Correct Option is D
Solution and Explanation
Step 1: Recall the formula for conditional probability
The conditional probability \( P(F|E) \) is given by: \[ P(F|E) = \frac{P(E \cap F)}{P(E)}. \] Step 2: Find \( P(E \cap F) \)
Using the formula for the probability of the union of two events: \[ P(E \cup F) = P(E) + P(F) - P(E \cap F). \] Substitute the given values \( P(E \cup F) = 0.4 \), \( P(E) = 0.1 \), \( P(F) = 0.3 \): \[ 0.4 = 0.1 + 0.3 - P(E \cap F). \] Simplify to find \( P(E \cap F) \): \[ P(E \cap F) = 0.1 + 0.3 - 0.4 = 0. \] Step 3: Calculate \( P(F|E) \)
Substitute \( P(E \cap F) = 0 \) and \( P(E) = 0.1 \) into the formula for \( P(F|E) \): \[ P(F|E) = \frac{P(E \cap F)}{P(E)} = \frac{0}{0.1} = 0. \] Step 4: Conclude the result
The conditional probability \( P(F|E) \) is \( 0 \). This indicates that the events \( E \) and \( F \) do not overlap.
Top CBSE CLASS XII Mathematics Questions
- 2, b, c are in A.P. and the range of determinant $\begin{vmatrix}1&1&1\\ 2&b&c\\ 4&b^{2}&c^{2}\end{vmatrix}$ is [2, 16]. Then find range of c is
- A committee of 11 members is to be formed from 8 males and 5 females. Let m denotes the number of ways of selecting committee having atleast 6 males and n denotes the number of ways of selecting atleast 3 females then
Determine whether each of the following relations are reflexive, symmetric, and transitive.
- Relation R in the set A={1,2,3,...13,14} defined as R={(x,y): 3x-y=0}.
- Relation R in the set of N natural numbers defined as R={(x,y): y=x+5 and x<4}.
- Relation R in the set A={1,2,3,4,5,6} defined as R={(x,y): y is divisible by x}.
- Relation R in the set of Z integers defined as R={(x,y): x-y is an integer}
- Relation R in the set of human beings in a town at a particular time given by
- R={(x,y): x and y work at same place}
- R={(x,y): x and y live in the same locality}
- R={(x,y): x is exactly 7 am taller that y}
- R={(x,y): x is wife of y}
- R={(x,y):x is father of y}
Show that the relation R in the set R of real numbers, defined as
R = {(a, b): a ≤ b2 } is neither reflexive nor symmetric nor transitive.Check whether the relation R defined in the set {1, 2, 3, 4, 5, 6} as
R = {(a, b): b = a + 1} is reflexive, symmetric or transitive.
Top CBSE CLASS XII Probability Questions
- A urn contains 5 red and 5 black balls.A ball is drawn at random,its colour is noted and is returned to the urn.Morever,2 additional balls of the colour drawn are put in the urn and then a ball is drawn at random.What is the probability that the second ball is red?
If P(A) = 0.8, P(B) = 0.5 and P(B|A) = 0.4, find:
- P(A∩B)
- P(A|B)
- P(A∪B)
- A bag contains 4 red and 4 black balls,another bag contains 2 red and 6 black balls.One of the two bags is selected at random and a ball is drawn from the bag which is found to be red.Find the probability that the ball is drawn from the first bag.
\(Evaluate \ P(A∩B)\ if \ 2P(A) = P(B) =\) \(\frac {5}{13}\) \(and \ P(A|B)=\) \(\frac 25\)
- Of the students in a college,it is known that \(60\%\) reside in hostel and \(40\%\) are day scholers.(not residing in hostel).Previous year result report that \(30\%\) of all students who reside in hostel attain A grade and \(20\%\) of day scholars attain A grade in their annual examination.At the end of the year,one student is choosen at random from the college and he has an A grade,What is the probability that the student is a hostler?
Top CBSE CLASS XII Questions
- 2, b, c are in A.P. and the range of determinant $\begin{vmatrix}1&1&1\\ 2&b&c\\ 4&b^{2}&c^{2}\end{vmatrix}$ is [2, 16]. Then find range of c is
- A boy of mass 50 kg is standing at one end of a, boat of length 9 m and mass 400 kg. He runs to the other, end. The distance through which the centre of mass of the boat boy system moves is
- A capillary tube of radius r is dipped inside a large vessel of water. The mass of water raised above water level is M. If the radius of capillary is doubled, the mass of water inside capillary will be
- A circular disc is rotating about its own axis. An external opposing torque 0.02 Nm is applied on the disc by which it comes rest in 5 seconds. The initial angular momentum of disc is
- A circular disc is rotating about its own axis at uniform angular velocity \(\omega.\) The disc is subjected to uniform angular retardation by which its angular velocity is decreased to \(\frac {\omega}{2}\) during 120 rotations. The number of rotations further made by it before coming to rest is