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(i) A prime number

(ii) A number lying between 2 and 6.

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Hint: To solve the question, we have to calculate the number of possible outcomes at the given conditions. To calculate probability divide the obtained number of outcomes to the total number of outcomes obtained when a dice is thrown.

Complete step-by-step answer:

The number of possible outcomes when a dice is thrown = 6

Since, a dice is a cube which is number 1, 2, 3, 4, 5, 6 on its 6 faces.

2, 3, 5 are the prime numbers among the numbers obtained when a dice is thrown.

Thus, the number of outcomes of getting a prime number when a dice is thrown = 3.

The probability of getting a prime number when a dice is thrown = Ratio of the number of outcomes of number between 2 and 6 prime number when a dice is thrown to the number of possible outcomes when a dice is thrown

\[=\dfrac{3}{6}\]

\[=\dfrac{1}{2}\]

\[\therefore \] The probability of getting a prime number when a dice is thrown \[=\dfrac{1}{2}=0.5\]

3,4,5 are the numbers between 2 and 6 which can be obtained when a dice is thrown.

Thus, the number of outcomes of getting a number between 2 and 6 when a dice is thrown = 3.

The probability of getting a number between 2 and 6 when a dice is thrown = Ratio of the number of outcomes of getting a number between 2 and 6 when a dice is thrown to the number of possible outcomes when a dice is thrown

\[=\dfrac{3}{6}\]

\[=\dfrac{1}{2}\]

\[\therefore \] The probability of getting a number between 2 and 6 when a dice is thrown \[=\dfrac{1}{2}=0.5\]

Note: The alternative quick method is that the answer for both the given cases will be the same since the number of required outcomes are equal.

Complete step-by-step answer:

The number of possible outcomes when a dice is thrown = 6

Since, a dice is a cube which is number 1, 2, 3, 4, 5, 6 on its 6 faces.

2, 3, 5 are the prime numbers among the numbers obtained when a dice is thrown.

Thus, the number of outcomes of getting a prime number when a dice is thrown = 3.

The probability of getting a prime number when a dice is thrown = Ratio of the number of outcomes of number between 2 and 6 prime number when a dice is thrown to the number of possible outcomes when a dice is thrown

\[=\dfrac{3}{6}\]

\[=\dfrac{1}{2}\]

\[\therefore \] The probability of getting a prime number when a dice is thrown \[=\dfrac{1}{2}=0.5\]

3,4,5 are the numbers between 2 and 6 which can be obtained when a dice is thrown.

Thus, the number of outcomes of getting a number between 2 and 6 when a dice is thrown = 3.

The probability of getting a number between 2 and 6 when a dice is thrown = Ratio of the number of outcomes of getting a number between 2 and 6 when a dice is thrown to the number of possible outcomes when a dice is thrown

\[=\dfrac{3}{6}\]

\[=\dfrac{1}{2}\]

\[\therefore \] The probability of getting a number between 2 and 6 when a dice is thrown \[=\dfrac{1}{2}=0.5\]

Note: The alternative quick method is that the answer for both the given cases will be the same since the number of required outcomes are equal.