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Mathematics

A die is thrown once. Find the probability of getting :

(i) a prime number

(ii) a number greater than 3

(iii) a number other than 3 and 5

(iv) a number less than 6

(v) a number greater than 6.

Probability

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Answer

(i) Total number of possible outcomes = 6 (i.e., 1, 2, 3, 4, 5, 6)

Number of favourable outcomes (Getting a prime number) = 3 (2, 3, 5)

P(Getting the prime number) = Number of favourable outcomesTotal number of possible outcomes\dfrac{\text{Number of favourable outcomes}}{\text{Total number of possible outcomes}}

= 36\dfrac{3}{6}

= 12\dfrac{1}{2}

Hence, the probability of getting the prime number is 12\dfrac{1}{2}.

(ii) Total number of possible outcomes = 6 (i.e., 1, 2, 3, 4, 5, 6)

Number of favourable outcomes (Getting a number greater than 3) = 3 (4, 5, 6)

P(Getting a number greater than 3) = Number of favourable outcomesTotal number of possible outcomes\dfrac{\text{Number of favourable outcomes}}{\text{Total number of possible outcomes}}

= 36\dfrac{3}{6}

= 12\dfrac{1}{2}

Hence, the probability of getting a number greater than 3 is 12\dfrac{1}{2}.

(iii) Total number of possible outcomes = 6 (i.e., 1, 2, 3, 4, 5, 6)

Number of favourable outcomes (Getting a number other than 3 and 5) = 4 (1, 2, 4, 6)

P(Getting a number other than 3 and 5) = Number of favourable outcomesTotal number of possible outcomes\dfrac{\text{Number of favourable outcomes}}{\text{Total number of possible outcomes}}

= 46\dfrac{4}{6}

= 23\dfrac{2}{3}

Hence, the probability of getting a number other than 3 and 5 is 23\dfrac{2}{3}.

(iv) Total number of possible outcomes = 6 (i.e., 1, 2, 3, 4, 5, 6)

Number of favourable outcomes (Getting a number less than 6) = 5 (1, 2, 3, 4, 5)

P(Getting a number less than 6) = Number of favourable outcomesTotal number of possible outcomes\dfrac{\text{Number of favourable outcomes}}{\text{Total number of possible outcomes}}

= 56\dfrac{5}{6}

Hence, the probability of getting a number less than 6 is 56\dfrac{5}{6}.

(v) Total number of possible outcomes = 6 (i.e., 1, 2, 3, 4, 5, 6)

Number of favourable outcomes (Getting a number greater than 6) = 0

P(Getting a number greater than 6) = Number of favourable outcomesTotal number of possible outcomes\dfrac{\text{Number of favourable outcomes}}{\text{Total number of possible outcomes}}

= 06\dfrac{0}{6}

= 0

Hence, the probability of getting a number greater than 6 is 0.

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