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An unbiased dice is rolled twice, what is the probability of not getting a 2 in any one of the two rolls?

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Last updated date: 13th Jun 2024
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Answer
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Hint: First find the probability of getting 2. After that subtract the value from 1 to get the probability of not getting 2. For the probability of not getting 2 in any one of the two rolls, square the probability of not getting 2 on one roll of the dice. Then solve it to get the desired result.

Complete step by step answer:
The total outcomes of the one dice are 6.
The probable outcome of getting 2 is,
$n\left( X=2 \right)=1$
Now, the probability of getting 2 is,
$\Rightarrow P\left( X=2 \right)=\dfrac{1}{6}$
Then, the probability of not getting 2 is,
$\Rightarrow P\left( X\ne 2 \right)=1-\dfrac{1}{6}$
Take the LCM,
$\Rightarrow P\left( X\ne 2 \right)=\dfrac{6-1}{6}$
Subtract 1 from 6 in the numerator of the right side,
$\Rightarrow P\left( X\ne 2 \right)=\dfrac{5}{6}$
Thus, for the 2 rolls, the probability will be,
$\Rightarrow P\left( X\ne 2\text{ in 2 roll} \right)=\dfrac{5}{6}\times \dfrac{5}{6}$
Multiply the terms,
$\Rightarrow P\left( X\ne 2\text{ in 2 roll} \right)=\dfrac{25}{36}$

Hence, option (A) is correct.

Note:
Probability is a measure of the likelihood of an event to occur. Many events cannot be predicted with total certainty. We can predict only the chance of an event to occur i.e. how likely they are to happen, using it.
The probability formula is defined as the possibility of an event to happen is equal to the ratio of the number of favorable outcomes and the total number of outcomes.
$P\left( E \right)=\dfrac{n\left( A \right)}{n\left( S \right)}$
A probability of 0 means that an event is impossible.
A probability of 1 means that an event is certain.
An event with a higher probability is more likely to occur.
Probabilities are always between 0 and 1.