Varbūtības teorija un matemātiskā statika

4.Uzdevums
P (no 14 metieniem trāpīs ne mazāk kā 5 reizes)= ‘’veiksmju skaits) m=5, 6, 7, 8,....15
1-P(no 14 metieniem trāpīs ne mazāk kā 5 reizes)= [m=0;m=1;m=2;m=3; m=4]
1-(P15,0(0.6)+ (P15,1(0.6)+ (P15,2(0.6)+ (P15,3(0.6)+ (P15,4(0.6))=
=1- (C_15^0*(0.6)^0*(0.4)^15+C_15^1*(0.6)^1*(0.4)^14+C_15^2*(0.6)^2*(0.4)^13+C_15^3*(0.6)^03*(0.4)^12+C_15^4*(0.6)^4*(0.4)^11 )=1-0.000025-0.0019-0.0074=0.99

C_15^0*(0.6)^0*(0.4)^15+C_15^1*(0.6)^1*(0.4)^14=0.415+15*0.6*0.414=
=0.0000011+9*0.0000027=0.000025
C_15^2*(0.6)^2*(0.4)^13+C_15^3*(0.6)^03*(0.4)^12=105*0.36*0.0000067+455*0.216*0.000017=0.0016+0.00025=0.0019
C_15^2=15!/2!(15-2)!=(15*14)/(1*2)=105
C_15^3=15!/3!(15-3)!=(15*14*13)/(1*2*3)=455
C_15^4*(0.6)^4*(0.4)^11=1365*0.13*0.000042=0.0074
C_15^4=15!/4!(15-4)!=(15*14*13*12)/(1*2*3*4)=1365
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