A fair dice is cast. A represents the probability of an even number appearing on the face and B represents the probability of a composite number appearing on the face. Are A and B independent events? ____

• When a fair dice is cast, the sample set is 1, 2, 3, 4, 5 and 6 where n(s) = 6.
  
  A: Probability of an even number - Favourable cases: 2, 4, 6.
  
  B: Probability of a composite number - Favourable cases: 4, 6 //Composite numbers are non-prime numbers//
  
  A intersection B = 4, 6
  
  P(A) = 3/6 = 1/2 and P(B) = 2/6 = 1/3.
  
  P(A intersection B) = 2/6 = 1/3 — (1)
  
  For A and B to be independent, P(A intersection B) = P(A) x P(B)
  
  P(A) X P(B) = (1/2) (1/3) = 1/6 — (2)
  
  Thus, A and B are not independent events as (1) is not equal to (2).
• 3 years agoHelpfull: Yes(3) No(0)