Question

Assertion : Two dice are thrown simultaneously. There are 11 possible outcomes (2,3,4,5,6,7,8,9,10,11,12) and each of them has a probability $\frac{1}{11}$.
Reason : Probability of an event (E) is defined as P(E) $=\frac{\text{Number of outcomes favourable to E}}{\text{Total number of possible outcomes}}$.

• A. Both assertion and reason are true and reason is the correct explanation of assertion.
• B. Both assertion and reason are true but reason is not the correct explanation of assertion.
• C. Assertion is true but reason is false.
• D. Assertion is false but reason is true.

Answer 1

The correct option is D

Assertion is false but reason is true.

If two dice will be thrown simultaneously then the total number of possible outcomes is 36 and probability of each outcome is not equal to $\frac{1}{11}$.
Probability of an event (E) is defined as P(E)
$=\frac{\text{Number of outcomes favourable to E}}{\text{Total number of possible outcomes}}$.
For example, probability of getting an even number on a die when a die is thrown
$=\frac{\text{Number of outcomes favourable to E}}{\text{Total number of possible outcomes}}$
$=\frac{3}{6}$
[$\because$ Here, the number of favourable outcomes will be 3 as 2, 4 and 6 are the possible even numbers ]
$\Rightarrow$Assertion : False
$\Rightarrow$Reason : True