4

8

pA=0.6
pB=0.7
pA0=0.4^3
pA1=0.4^2 * 0.6 * choose(3,1)
pA2=0.4 * 0.6^2 * choose(3,2)
pA3=0.6^3
pB0=0.3^3
pB1=0.3^2 * 0.7 *choose(3,1)
pB2=0.3 * 0.7^2 *choose(3,2)
pB3=0.7^3

ans1= pA0*pB0+pA1*pB1+pA2*pB2+pA3*pB3
ans1
# [1] 0.32076

ans2= (1-pA0)*pB0+(1-pA0-pA1)*pB1+pA3*pB2
ans2
# [1] 0.243

15

ans = 0 
p = 0.0015
k = 0
while(k <= 10){
    ans = ans + choose(5000, k) * p^k * (1 - p)^(5000 -k)
    k = k + 1
}
ans
[1] 0.8623991

18