1-

$P(B) = C(4,2) * p^2 * (1-p)^2$

0 or 1 times

$P(C) = (1-p)^4 + C(4,1) * p * (1 - p)^3$

3 or 4 times

$P(D) = p^3 * (1-p) * C(4,3) + p^4$

$P(E) = 1 - (1-p)^4$

2-

$P(B) = C(n,m) * p^{m} * (1-p)^55$
$P(B) = C(100,35) * 0.3^{35} * (0.7)^65$

$P(CC) = \displaystyle \sum_{i=m_1}^{i=m_2} C(n,i)*p^i*(1-p)^{(n-i)}$
$P(CC) = C(100,25)*0.3^{25} * 0.7^{75} + C(100,26)*0.3^{26}*0.7^{74} + C(100,27)*0.3^{27}*0.7^{73} + C(100,28)*0.3^{28}*0.7^{72} \ldots$ continue yourself to 32

3-

$P(B)=C(n,2)*p^2*(1-p)^{(n-2)}$
$P(B)=C(1000,2)*0.0025^2*0.9975^{998}$

$P(C)= (1-p)^n + C(n,1)*p*(1-p)^{(n-1)}$
$P(C)= 0.9975^{1000} + 1000 * 0.0025 * 0.9975^{999}$

$P(D)= 1 - P(B) - P(C)$