Natasha Awada, Paul La Rondie, Laurie Buchanan and, Jill Stevens Solutions for Chapter: Quantifying Randomness: Probability, Exercise 20: Exercise 8G

Given that, $\mathrm{P}\left(E^{\text{'}}\right)=\mathrm{P}\left(F\right)=0.6$ and $\mathrm{P}(E\cap F)=0.24$.

Write down $P\left(E\right)$.

Given that, $\mathrm{P}\left(E^{\text{'}}\right)=\mathrm{P}\left(F\right)=0.6$ and $\mathrm{P}(E\cap F)=0.24$.

Explain how you know $E$ and $F$ are independent.

Given that, $\mathrm{P}\left(E^{\text{'}}\right)=\mathrm{P}\left(F\right)=0.6$ and $\mathrm{P}(E\cap F)=0.24$.

Explain how you know $E$ and $F$ are not mutually exclusive.

Given that, $\mathrm{P}\left(E^{\text{'}}\right)=\mathrm{P}\left(F\right)=0.6$ and $\mathrm{P}(E\cap F)=0.24$.

Find $\mathrm{P}\left(E\cup F^{\text{'}}\right)$.

A six sided dice is numbered $1,2,2,5,5,6$. It is thrown three times. What is the probability that the scores add up to $6$?

$A$ and $B$ are two independent events such that $P\left(A\right)=0.9$ and $P\left(B\right)=0.3$. Find $P\left(A\cap B\right)$.

$A$ and $B$ are two independent events such that $P\left(A\right)=0.9$ and $P\left(B\right)=0.3$. Find $P\left(A\cap B^{\text{'}}\right)$.

$A$ and $B$ are two independent events such that $P\left(A\right)=0.9$ and $P\left(B\right)=0.3$. Find $P\left(A\cup B^{\text{'}}\right)$.