Dean Chalmers and Julian Gilbey Solutions for Chapter: Probability, Exercise 6: EXERCISE 4D

Two independent events are $M$ and $N .$ Given that $\mathrm{P}\left(M\right)=0.75$ and $\mathrm{P}(M\cap N)=0.21$, find $\mathrm{P}\left(N\right).$

Independent events $S$ and $T$ are such that $\mathrm{P}\left(S\right)=0.4$ and $\mathrm{P}\left(T^{\text{'}}\right)=0.2$. Find:

$\mathrm{P}(S\cap T)$

Independent events $S$ and $T$ are such that $\mathrm{P}\left(S\right)=0.4$ and $\mathrm{P}\left(T^{\text{'}}\right)=0.2$. Find:

$\mathrm{P}\left(S^{\text{'}}\cap T\right).$

$A, B$ and $C$ are independent events, and it is given that $\mathrm{P}(A\cap B)=0.35$, $\mathrm{P}(B\cap C)=0.56$ and $\mathrm{P}(A\cap C)=0.4$.

Express $\mathrm{P}\left(A\right)$ in terms of $\mathrm{P}\left(B\right)$.

$A, B$ and $C$ are independent events, and it is given that $\mathrm{P}(A\cap B)=0.35$, $\mathrm{P}(B\cap C)=0.56$ and $\mathrm{P}(A\cap C)=0.4$.

Express $\mathrm{P}\left(A\right)$ in terms of $\mathrm{P}\left(C\right).$

$A, B$ and $C$ are independent events, and it is given that $\mathrm{P}(A\cap B)=0.35$, $\mathrm{P}(B\cap C)=0.56$ and $\mathrm{P}(A\cap C)=0.4$.

Find $\mathrm{P}\left(B\right)$.

$A, B$ and $C$ are independent events, and it is given that $\mathrm{P}(A\cap B)=0.35$, $\mathrm{P}(B\cap C)=0.56$ and $\mathrm{P}(A\cap C)=0.4$.

Find $\mathrm{P}\left(A^{\text{'}}\right)$.

$A, B$ and $C$ are independent events, and it is given that $\mathrm{P}(A\cap B)=0.35$, $\mathrm{P}(B\cap C)=0.56$ and $\mathrm{P}(A\cap C)=0.4$.

Find $\mathrm{P}\left({\mathrm{B}}^{\text{'}}\cap {\mathrm{C}}^{\text{'}}\right)$.