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4 marksTree diagram — without replacement4MA1 style 🔢 Calculator
A bag contains 5 red and 3 blue counters. Two counters are taken without replacement. Calculate (a) P(both red) (b) P(one of each colour). (4 marks)
Hint: (a) Multiply the two branch probabilities. After taking one red, there are 4 red out of 7 remaining. (b) Two routes: R then B, or B then R — multiply each route then add.
+40 XP
4 marksVenn diagram problemGrade 7 Booklet style ✏️ No calculator
In a class of 30 students: 18 study French (F), 12 study Spanish (S), 5 study both. (a) Draw a Venn diagram and fill in all regions. (b) P(student studies French but not Spanish). (c) P(studies neither). (4 marks)
Hint: Fill in the intersection (both) first: 5. Then: only F = 18−5, only S = 12−5. Neither = total − all in circles.
+40 XP
4 marksConditional probability4MA1 style ✏️ No calculator
Two events A and B. P(A) = 0.6, P(B) = 0.5, P(A ∩ B) = 0.3. (a) Find P(A ∪ B). (b) Find P(A|B). (c) Are A and B independent? Explain. (4 marks)
Hint: (a) Addition rule. (b) P(A|B) = P(A∩B)/P(B). (c) A and B are independent if P(A|B) = P(A). Check if this holds.
+40 XP
1 markExpected frequency4MA1 style
A biased coin gives heads with probability 0.35. If flipped 200 times, what is the expected number of heads?
A 35
B 65
C 70
D 100
1 markMutually exclusive events4MA1 style
Events A and B are mutually exclusive. P(A) = 0.3 and P(B) = 0.25. What is P(A or B)?