1.

A die is thrown at random. Find the probability of getting (i) 2 (ii) a number less than 3 (iii) a composite number (iv) a number not less than 4.

Answer»

(i) Total number of outcomes = 6 (they are 1,2,3,4,5,6) 

Chances of getting 2 on the die = 1

Probability (P) = \(\frac{Number\,of\,favorable\,outcomes}{Total\,number\,of\,outcomes}\)

∴ Probability of getting 2 on die P(2)

\(\frac{possible\,chances\,of\,getting\,2}{Total\,number\,of\,outcomes}\) = \(\frac{1}{6}\)

(ii) Total number of outcomes = 6 (they are 1,2,3,4,5,6) 

Chances of getting a number less than 3 on the die = 2 (They are 1,2)

Probability (P) = \(\frac{Number\,of\,favorable\,outcomes}{Total\,number\,of\,outcomes}\)

∴ Probability of getting a number less than 3 on die P(less than 3)

\(\frac{Possible\,chances\,of\,getting\,a\,number\,less\,than\,3}{Total\,number\,of\,outcomes}\) = \(\frac{2}{6}=\frac{1}{3}\)

(iii) Total number of outcomes = 6 (they are 1,2,3,4,5,6) 

Composite number: A number which is not a prime number or a number which is divisible by numbers other than 1 and the number itself. 

Chances of getting a composite number on the die = 2 (They are 4,6)

Probability (P) = \(\frac{Number\,of\,favorable\,outcomes}{Total\,number\,of\,outcomes}\)

∴ Probability of getting a composite number on die the P(composite number)

\(\frac{Possible\,chances\,of\,getting\,a\,number\,less\,than\,3}{Total\,number\,of\,outcomes}\) = \(\frac{2}{6}=\frac{1}{3}\)

(iv) Total number of outcomes = 6 (they are 1,2,3,4,5,6) 

Chances of getting a number not less than 4 on the die = 4 (They are 4,5,6)

Probability (P) = \(\frac{Number\,of\,favorable\,outcomes}{Total\,number\,of\,outcomes}\)

∴ Probability of getting a number not less than 4 on die P(not less than 4)

\(\frac{Possible\,chances\,of\,getting\,a\,number\,less\,than\,3}{Total\,number\,of\,outcomes}\) = \(\frac{3}{6}=\frac{1}{2}\)



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