##1.a.-c.

sensitivity <- (.9*.94)
sensitivity
## [1] 0.846
false_negative <- (.9*.06)
false_negative
## [1] 0.054
false_positive <- (.1*.1)
false_positive
## [1] 0.01
specificity <- (.9*.1)
specificity
## [1] 0.09
ptest_pos<-sensitivity+false_positive
ptest_pos
## [1] 0.856
ptruepos_iftestpos <- (sensitivity/ptest_pos)
ptruepos_iftestpos
## [1] 0.9883178

##2. a.-c. Learn to loop through j<-1 to j<-6 with ++1 interval 

y0<- dbinom(0, 6, .24); y0
## [1] 0.1926999
y1<- dbinom(1, 6, .24); y1
## [1] 0.3651157
y2<- dbinom(2, 6, .24); y2
## [1] 0.2882492
y3<- dbinom(3, 6, .24); y3
## [1] 0.1213681
y4<- dbinom(4, 6, .24); y4
## [1] 0.02874507
y5<- dbinom(5, 6, .24); y5
## [1] 0.003630957
y6<- dbinom(6, 6, .24); y6
## [1] 0.000191103
"binomial coefficients for n=6"
## [1] "binomial coefficients for n=6"
n<-6
j<-1
factorial(n)/(factorial(j)*factorial(n-j))
## [1] 6
n<-6
j<-2
factorial(n)/(factorial(j)*factorial(n-j))
## [1] 15
n<-6
j<-3
factorial(n)/(factorial(j)*factorial(n-j))
## [1] 20
n<-6
j<-4
factorial(n)/(factorial(j)*factorial(n-j))
## [1] 15
n<-6
j<-5
factorial(n)/(factorial(j)*factorial(n-j))
## [1] 6
n<-6
j<-6
factorial(n)/(factorial(j)*factorial(n-j))
## [1] 1
PYgtoe_3 <-(y3+y4+y5+y6); PYgtoe_3
## [1] 0.1539352
PYltoe_2 <-(y0+y1+y2);PYltoe_2
## [1] 0.8460648