KVPY2017MathematicsProbability
Consider the following events; E ₁: Six fair dice are rolled and at least one die shows six. E ₂ : Twelve fair dice are rolled and at least two dice show six. Let p ₁ be the probability of E ₁ and p ₂ be the probability of E ₂ . Which of the following is true?
Options
- Ap ₁> p ₂
- Bp₁=p₂=0.6651
- Cp ₁ < p ₂
- Dp₁=p₂=0.3349
Correct answer
A. p ₁> p ₂
Step-by-step solution
aligned p ₁=& 1-( no die show six ) & 1- ( ( 5 6 )⁶ )=0.6651 p ₂=& 1-( no die shown two + one die shown two ) p ₂=& 1- [ ( 5 6 )¹²+ ¹² C ₁ ( 5 6 )¹¹ ( 1 6 )¹ ] =& 0.61866 p ₁>& p ₂ aligned