Determine P(X=k) for a certain k and for X following a given binomial distribution, using the formula Statistics & Probabilities

X follows \mathcal{B}\left(4{,}0.2\right). Determine P\left(X=3\right).

P\left(X=3\right)=\dfrac{16}{625}

P\left(X=3\right)=\dfrac{256}{625}

P\left(X=3\right)=\dfrac{16}{25}

P\left(X=3\right)=\dfrac{4}{25}

X follows \mathcal{B}\left(3{,}0.5\right). Determine P\left(X=2\right).

P\left(X=2\right)=\dfrac{3}{8}

P\left(X=2\right)=\dfrac{5}{8}

P\left(X=2\right)=\dfrac{1}{2}

P\left(X=2\right)=\dfrac{3}{4}

X follows \mathcal{B}\left(4{,}0.3\right). Determine P\left(X=1\right).

P\left(X=1\right)=\dfrac{1\ 029}{2\ 500}

P\left(X=1\right)=\dfrac{571}{2\ 500}

P\left(X=1\right)=\dfrac{3}{40}

P\left(X=1\right)=\dfrac{571}{1\ 250}

X follows \mathcal{B}\left(5{,}0.4\right). Determine P\left(X=3\right).

P\left(X=3\right)=\dfrac{6}{25}

P\left(X=3\right)=\dfrac{144}{625}

P\left(X=3\right)=\dfrac{72}{125}

P\left(X=3\right)=\dfrac{24}{125}

X follows \mathcal{B}\left(4{,}0.1\right). Determine P\left(X=2\right).

P\left(X=2\right)=\dfrac{243}{5\ 000}

P\left(X=2\right)=\dfrac{121}{250}

P\left(X=2\right)=\dfrac{1}{20}

P\left(X=2\right)=\dfrac{121}{750}

X follows \mathcal{B}\left(6{,}0.5\right). Determine P\left(X=4\right).

P\left(X=4\right)=\dfrac{15}{64}

P\left(X=4\right)=\dfrac{1}{3}

P\left(X=4\right)=\dfrac{2}{3}

P\left(X=4\right)=\dfrac{45}{128}