X and Y are two events in the sample space S such that P X = 3 4 , P Y = 5 8 and P X ∩ Y = 1 2 . Then find the value of P X ∪ Y

Given that: P X = 3 4 , P Y = 5 8 and P X ∩ Y = 1 2 . To find the value of P X ∪ Y We know that P X ∩ Y = P X + P Y - P X ∪ Y ⇒ P X ∪ Y = P X + P Y - P X ∩ Y On putting the value of P X ∩ Y , P X & P Y we get ⇒ P X ∪ Y = 3 4 + 5 8 - 1 2 ⇒ P X ∪ Y = 6 + 5 - 4 8 ⇒ P X ∪ Y = 7 8 Hence, the value of P X ∪ Y is 7 8

X and Y are two events in the sample space S such that P X = 3 4 , P Y = 5 8 and P X ∩ Y = 1 2 . Then find the value of P X ∪ Y

Given that: P X = 3 4 , P Y = 5 8 and P X ∩ Y = 1 2 . To find the value of P X ∪ Y We know that P X ∩ Y = P X + P Y - P X ∪ Y ⇒ P X ∪ Y = P X + P Y - P X ∩ Y On putting the value of P X ∩ Y , P X & P Y we get ⇒ P X ∪ Y = 3 4 + 5 8 - 1 2 ⇒ P X ∪ Y = 6 + 5 - 4 8 ⇒ P X ∪ Y = 7 8 Hence, the value of P X ∪ Y is 7 8

X and Y are two events in the sample space S such that P X = 3 4 , P Y = 5 8 and P X ∩ Y = 1 2 . Then find the value of P X c

Given that: P X = 3 4 , P Y = 5 8 and P X ∩ Y = 1 2 . To find the value of P X c We know that P X + P X c = 1 On putting the value of P X we get ⇒ 3 4 + P X c = 1 ⇒ P X c = 1 - 3 4 ⇒ P X c = 4 - 3 4 ⇒ P X c = 1 4 Hence, the value of P X c is 1 4 .

The probabilities of solving a mathematical problem by Gopal, Gour and Kesto are 1 2 , 1 3 & 1 4 respectively. Find the probability of not solving the problem.

Let the event of solving the problem by Gopal be A , event of solving the problem by Gour be B , and event of solving the problem by Kesto be C . So P A = 1 2 , P B = 1 3 & P C = 1 4 . Now the probability of not solving the problem can be represented by P A c ∩ B c ∩ C c P A c ∩ B c ∩ C c = P A c × P B c × P C c = 1 - P A × 1 - P B × 1 - P C = 1 - 1 2 × 1 - 1 3 × 1 - 1 4 = 2 - 1 2 × 3 - 1 3 × 4 - 1 4 = 1 2 × 2 3 × 3 4 = 1 4 Hence, the probability of not solving the problem is 1 4 .

E M B I B E

MATHEMATICS CLASS 9>Chapter 25 - Probability>EXERCISE-2>Q 5

MEDIUM

9th West Bengal Board

IMPORTANT

Earn 100

$X$ and $Y$ are two events in the sample space $S$ such that $P (X) = \frac{3}{4}, P (Y) = \frac{5}{8}$ and $P (X \cap Y) = \frac{1}{2}$ .

Then find the value of $P (X \cup Y)$

Important Questions on Probability

EASY

9th West Bengal Board

IMPORTANT

MATHEMATICS CLASS 9>Chapter 25 - Probability>EXERCISE-2>Q 5

$X$ and $Y$ are two events in the sample space $S$ such that $P (X) = \frac{3}{4}, P (Y) = \frac{5}{8}$ and $P (X \cap Y) = \frac{1}{2}$ .

Then find the value of $P (X^{c})$

EASY

9th West Bengal Board

IMPORTANT

MATHEMATICS CLASS 9>Chapter 25 - Probability>EXERCISE-2>Q 6

Two unbiased coins are tossed one time. Find the probability of occurring two tails.

EASY

9th West Bengal Board

IMPORTANT

MATHEMATICS CLASS 9>Chapter 25 - Probability>EXERCISE-2>Q 7

An unbiased dice is rolled one time. Find the probability of occurring

4

.

MEDIUM

9th West Bengal Board

IMPORTANT

MATHEMATICS CLASS 9>Chapter 25 - Probability>EXERCISE-2>Q 8

The probabilities of solving a mathematical problem by Gopal, Gour and Kesto are $\frac{1}{2}, \frac{1}{3} & \frac{1}{4}$ respectively. Find the probability of not solving the problem.