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Probability and Probability Distributions · Paper 1 — Free Maths AA SL Practice Questions

1FoundationSAQ-SBasic probability rules and conceptss5 marksPaper 1~8 min
In a school survey, 60 students were asked if they play football (FF) or basketball (BB). The results show that 35 play football, 22 play basketball, and 12 play both sports.
(a)
Find the probability that a randomly chosen student plays neither sport. [2 marks]
(b)
Given that a student plays basketball, find the probability that they also play football. [2 marks]
(c)
Determine whether playing football and playing basketball are independent events. Justify your answer. [1 mark]
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Solutions

2FoundationSAQ-SBasic probability rules and conceptss5 marksPaper 1~8 min
Events XX and YY are such that P(X)=0.6P(X) = 0.6, P(Y)=0.3P(Y) = 0.3, and P(X∩Y)=0.2P(X \cap Y) = 0.2.
(a)
Find P(X∪Y)P(X \cup Y). [2 marks]
(b)
Find P(Y∩X′)P(Y \cap X'). [2 marks]
(c)
Determine whether XX and YY are independent. Justify your answer. [1 mark]
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Solutions

3MasterySAQ-SBasic probability rules and conceptss5 marksPaper 1~8 min
In a school, 60%60\% of students play basketball and 45%45\% play volleyball. It is known that 30%30\% of students play both sports.
(a)
Show that the probability that a randomly selected student plays neither sport is 0.250.25. [3 marks]
(b)
Given that a randomly selected student plays at least one of the two sports, find the probability that they play both sports. [2 marks]
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Solutions

4ChallengeSAQ-LBasic probability rules and conceptss10 marksPaper 1~15 min
A bag contains 5 red marbles and 3 blue marbles. Two marbles are drawn at random without replacement. Let RR be the event that the first marble drawn is red. Let BB be the event that the second marble drawn is blue.
(a)
Determine P(R∩B)\mathrm{P}(R \cap B). [2 marks]
(b)
Determine P(B)\mathrm{P}(B). [3 marks]
(c)
Determine P(R∪B)\mathrm{P}(R \cup B). [2 marks]
(d)
Determine whether events RR and BB are independent. Justify your answer with a calculation, and explain what your result means in the context of this experiment. [3 marks]
diagram

Solutions

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