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Four fair dice D1 ,D2 , D3 ,D4 are rolled simultaneously . What is the probability that D4 shows a number appearing on one of D1 , D2 & D3?

Four fair dice D1 ,D2 , D3 ,D4 are rolled simultaneously . What is the probability that D4 shows a number appearing on one of D1 , D2 & D3?

Grade:11

1 Answers

Arun
25758 Points
4 years ago
Total   no .   of   outcomes = 6 4
Favourable cases are:-when 4D and only 1 of 1D2D3D shows same number or only 2 of 1D2D3D shows same numberor all 3 of 1D2D3D shows same number.
No. of favorable outcomes=61C×31C×5×5+61C×32C×5+61C×33C                
 =61C+C335×32C+5×5×31C
So, Required probability=outcomes of .no Totaloutcomes favorable of .No=4633C+5×32C+5×5×31C61C               
  =6×2161+5×3+25×3×6=21691 

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