Assertion - Two dice are thrown simultaneously- There are 11 possible outcomes and each of them has a probability 1-11-Reason - Probability of an event E is defined as PE -Number of favourable outcomes-Total number of possible outcomes-

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Sum of Probabilities

Assertion : T...

Question

Assertion : Two dice are thrown simultaneously. There are 11 possible outcomes and each of them has a probability $\frac{1}{11}$ .
Reason : Probability of an event (E) is defined as P(E) $= \frac{N u m b e r o f f a v o u r a b l e o u t c o m e s}{T o t a l n u m b e r o f p o s s i b l e o u t c o m e s}$ .

Both assertion and reason are true and reason is the correct explanation of assertion.

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Both assertion and reason are true but reason is not the correct explanation of assertion.

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Assertion is true but reason is false.

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Assertion is false but reason is true.

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Solution

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 (6 x 6) and probability of each outcome is equal to $\frac{1}{36}$ .
Probability of an event (E) is defined as P(E)
$= \frac{N u m b e r o f f a v o u r a b l e o u t c o m e s}{T o t a l n u m b e r o f p o s s i b l e o u t c o m e s}$ .
$\Rightarrow$ Assertion : False
$\Rightarrow$ Reason : True

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Similar questions

Q. Assertion : Two dice are thrown simultaneously. There are 11 possible outcomes and each of them has a probability

\frac{1}{11}

.
Reason : Probability of an event (E) is defined as P(E)

= \frac{N u m b e r o f f a v o u r a b l e o u t c o m e s}{T o t a l n u m b e r o f p o s s i b l e o u t c o m e s}

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) $= \frac{Number of outcomes favourable to E}{Total number of possible outcomes}$ .

A student argues that there are

11

possible outcomes (sum of numbers on both dice)

2, 3, 4, 5, 6, 7, 8, 9, 10, 11

and

12

when we throws two dice simultaneously. Therefore each of them has a probability

\frac{1}{11} .

Do you agree with this argument? Justify your answer.

Theoretical probability of an event A is given as $\frac{A}{B}$ where

S1 : A is the number of outcomes favourable to E

S2 : B is the total number of possible outcomes.

Which of the following arguments are correct and which are not correct? Give reasons for your answer.

(i) If two coins are tossed simultaneously there are three possible outcomes−−two heads, two tails or one of each. Therefore, for each of these outcomes, the probability is.

(ii) If a die is thrown, there are two possible outcomes−−an odd number or an even number. Therefore, the probability of getting an odd number is.

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Assertion : Two dice are thrown simultaneously. There are 11 possible outcomes and each of them has a probability 111. Reason : Probability of an event (E) is defined as P(E) =Number of favourable outcomesTotal number of possible outcomes.