1. 1. Bob shops at a market each week. The event that

Bob buys carrots is denoted by \(C\)
Bob buys onions is denoted by \(O\)
At each visit, Bob may buy neither, or one, or both of these items. The probability that Bob buys carrots is 0.65
Bob does not buy onions is 0.3
Bob buys onions but not carrots is 0.15
The Venn diagram below represents the events \(C\) and \(O\)
\includegraphics[max width=\textwidth, alt={}, center]{f94b29e0-081f-45e8-99a7-ac835eec91e5-10_453_851_877_607}
where \(w , x , y\) and \(z\) are probabilities.

1. Find the value of \(w\), the value of \(x\), the value of \(y\) and the value of \(z\) For one visit to the market,
2. find the probability that Bob buys either carrots or onions but not both.
3. Show that the events \(C\) and \(O\) are not independent.
   (ii) \(F , G\) and \(H\) are 3 events. \(F\) and \(H\) are mutually exclusive. \(F\) and \(G\) are independent. Given that $$\mathrm { P } ( F ) = \frac { 2 } { 7 } \quad \mathrm { P } ( H ) = \frac { 1 } { 4 } \quad \mathrm { P } ( F \cup G ) = \frac { 5 } { 8 }$$
4. find \(\operatorname { P } ( F \cup H )\)
5. find \(\mathrm { P } ( G )\)
6. find \(\operatorname { P } ( F \cap G )\)