A-LevelMathematicsProbability and statistics9709/62 · May/June 2017 · Q79 Marks
During the school holidays, each day Khalid either rides on his bicycle with probability 0.6, or on his skateboard with probability 0.4. Khalid does not ride on both on the same day. If he rides on his bicycle then the probability that he hurts himself is 0.05. If he rides on his skateboard the probability that he hurts himself is 0.75.
- (i)Find the probability that Khalid hurts himself on any particular day.[2]
- (ii)Given that Khalid hurts himself on a particular day, find the probability that he is riding on his skateboard.[2]
- (iii)There are 45 days of school holidays. Show that the variance of the number of days Khalid rides on his skateboard is the same as the variance of the number of days that Khalid rides on his bicycle.[2]
- (iv)Find the probability that Khalid rides on his skateboard on at least 2 of 10 randomly chosen days in the school holidays.[3]
Mark scheme
Marking points from the official mark scheme (May/June 2017). The mark or mark type is shown in brackets.
- M1 Summing two 2-factor probs using 0.6 with 0.05 or 0.95, and 0.4 with 0.75 or 0.25
- A1 Correct final answer accept 0.33
- M1 FT Their P(S∩H) / Their P(H) unsimplified, FT from (i)
- A1
- B1 One variance stated unsimplified
- B1 Second variance stated unsimplified and at least one variance clearly identified, and both evaluated or showing equal or conclusion made
- SR B1 - Standard Deviation calculated Fulfil all the criteria for the variance method but calculated to Standard Deviation
- M1 Bin term ¹⁰Cx pˣ (1-p)¹⁰⁻ˣ 0 <p<1
- M1 Correct unsimplified answer
- A1
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