Question

Probability

Answer 1

I know that \[\Large P(R|S)=0.5 \] \[\Large P(R|S)=\frac{P(R ~\cap S)}{P(S)}=\frac{P(R ~\cap S)}{0.6}\]
And so \[\Large P(R~ \cap S)=0.5 \]

Answer 2

So this is as far as I am

Answer 3

@Miracrown

Answer 4

\( P(R|S') = \frac{P(R \;\cap\;S')}{P(S')} = \frac{P(R-S)}{1-0.6}\)
So, \( P(R-S)=0.4\times0.4=0.16\) \( \therefore P(R)=P(R-S)+P(R\;\cap\;S)=0.16+0.3=0.46\;\; \boxed{} \)

Answer 5

\( P(S|R) = \frac{P(S\;\cap\;R)}{P(R)}=\frac{0.3}{0.46}=\frac{15}{23}\;\;\boxed{} \)

Answer 6

\( P(S'|R)=\frac{P(S'\;\cap\;R)}{P(R)}= \frac{0.16}{0.46}=\frac{8}{23}\;\;\boxed{}\)

Answer 7

\(P(S'|R')=\frac{P(S'\;\cap\;R')}{P(R')}=\frac{P((R\;\cup\;S)')}{1-0.46}=\frac{1-P(R)-P(S)+P(R\;\cap\;S)}{0.54}=\frac{1-0.46-0.6+0.3}{0.54}=\frac{0.24}{0.54}=\frac49\;\;\boxed{} \)