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Sasha is trying to remember a 4-digit pin number - OCR - GCSE Maths - Question 12 - 2023 - Paper 2

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Sasha is trying to remember a 4-digit pin number. Sasha knows it has the following digits and that the first digit is 9. 9 3 2 7 (a) Write down all of the possible... show full transcript

Worked Solution & Example Answer:Sasha is trying to remember a 4-digit pin number - OCR - GCSE Maths - Question 12 - 2023 - Paper 2

Step 1

Write down all of the possible orders for Sasha’s 4-digit pin number.

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Answer

Given the digits 9, 3, 2, and 7, with the first digit fixed as 9, the possible 4-digit PIN numbers are ordered permutations of the remaining digits:

  1. 9327
  2. 9372
  3. 9237
  4. 9273
  5. 9732
  6. 9723

Thus, the possible orders for Sasha's 4-digit PIN number are:

  • 9327
  • 9372
  • 9237
  • 9273
  • 9732
  • 9723

Step 2

Write down the probability that the last digit of the pin number that Sasha tries is 2.

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Answer

Out of the 6 possible PIN numbers derived from the previous step, only the combinations 9327 and 9372 have 2 as the last digit. Therefore, the probability can be calculated as:

extProbability=extNumberofsuccessfuloutcomesextTotaloutcomes=26=13 ext{Probability} = \frac{ ext{Number of successful outcomes}}{ ext{Total outcomes}} = \frac{2}{6} = \frac{1}{3}

Hence, the probability that the last digit of the pin number that Sasha tries is 2 is ( \frac{1}{3} ).

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