A die is thrown. Let be the event that the number obtained is greater than 3. Let be the event that the number obtained is less than 5. Then is [2008]

Question

A die is thrown. Let $A$ be the event that the number obtained is greater than 3. Let $B$ be the event that the number obtained is less than 5. Then $P (A \cup B)$ is [2008]

Smart Achievers · Accepted Answer

(3)

$A (number is greater than 3) = {4, 5, 6}$

$\Rightarrow P (A) = \frac{3}{6} = \frac{1}{2}$

$B (number is less than 5) = {1, 2, 3, 4} \Rightarrow P (B) = \frac{4}{6} = \frac{2}{3}$

$∴$ $A \cap B = {4} \Rightarrow P (A \cap B) = \frac{1}{6}$

$∴$ $P (A \cup B) = P (A) + P (B) - P (A \cap B)$

$= \frac{1}{2} + \frac{2}{3} - \frac{1}{6} = \frac{3 + 4 - 1}{6} = 1$

Solution

Q.
A die is thrown. Let $A$ be the event that the number obtained is greater than 3. Let $B$ be the event that the number obtained is less than 5. Then $P (A \cup B)$ is [2008]

1 $\frac{3}{5}$

2 $0$

3 $1$

4 $\frac{2}{5}$

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Solution

Q. A die is thrown. Let A be the event that the number obtained is greater than 3. Let B be the event that the number obtained is less than 5. Then P(A∪B) is [2008]

1 35

2 0

3 1

4 25