15. At breakfast, the probability that Stefan has a bowl of cereal is 0·7. The probability of Stefan having a slice of toast for breakfast is independent of him having a bowl of cereal. The probability that Stefan has a bowl of cereal and a slice of toast is 0·28.
(a) Complete the tree diagram. [4]
(b) Find the probability that Stefan has neither cereal nor toast for breakfast. [2]
Mark scheme (a)
Scheme
Marks
Comments
0.3 indicated for no cereal
B1
In working or on tree
Idea \(0.7 \times \ldots = 0.28\)
M1
P(toast) = 0.4
A1
In working or on tree
Second branches 0.4 0.6 0.4 0.6
B1
FT from their P(toast) provided M1 awarded
Mark scheme (b)
Scheme
Marks
Comments
\(0.3 \times 0.6\)
M1
FT ‘their 0.3’ × ‘their 0.6’ from their lowest branches in (a)
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