AP EAMCET2008MathematicsProbability
Let S be the sample space of the random experiment of throwing simultaneously two unbiased dice with six faces (numbered 1 to 6 ) and let E_k= (a, b) S: a b=k for k 1 . If p_k+P (E_k ) for k 1 , then the correct among the following, is
Options
- Ap₁ < p₃₀ < p₄ < p₆
- Bp₃₆ < p₆ < p₂ < p₄
- Cp₁ < p₁₁ < p₄ < p₆
- Dp₃₆ < p₁₁ < p₆ < p₄
Correct answer
A. p₁ < p₃₀ < p₄ < p₆
Step-by-step solution
Given that, E_k= (a, b) S: a b=k for k 1 and p_k=P (E_k ) Now, E₁= (1,1) p₁=P (E₁ ) aligned & p₁= 1 36 & E₂= (1,2),(2,1) p₂=P (E₂ ) & p₂= 2 36 & E₄= (1,4),(4,1),(2,2) p₄=P (E₄ ) & p₄= 3 36 & E₆= (1,6),(6,1),(2,3),(3,2) & p₆=P (E₆ ) p₆= 4 36 & and E₃₀= (5,6),(6,5) p₃₀=P (E₃₀ ) & p₃₀= 2 36 aligned From the above results, we get p₁ < p₃₀ < p₄ < p₆ Hence, option (1) is correct.