Gr 12 Mathematics: Ch 9.6 Application to Probability Problems
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Questions and Answers

What is the formula to calculate the probability of an event E?

  • P(E) = n(E) - n(S)
  • P(E) = n(E) / n(S) (correct)
  • P(E) = n(E) × n(S)
  • P(E) = n(S) / n(E)

    • If a PIN consists of 4 digits and digits can be repeated, how many possible PINs are there?

  • 1,000
  • 5,000
  • 15,000
  • 10,000 (correct)

    • If a PIN consists of 4 digits and digits cannot be repeated, how many possible PINs are there?

  • 3,024
  • 4,000
  • 6,561
  • 5,040 (correct)

    • What is the probability that a PIN contains at least one 8 if digits can be repeated?

    <p>0.3439</p> Signup and view all the answers

    What is the probability that a PIN contains at least one 8 if digits cannot be repeated?

    <p>0.4</p> Signup and view all the answers

    How many letters are excluded when forming a car number plate consisting of 3 letters?

    <p>6</p> Signup and view all the answers

    What is the total number of possible car number plates?

    <p>20,736</p> Signup and view all the answers

    What is the total number of possible digits for a car number plate?

    <p>1,000,000</p> Signup and view all the answers

    What is the total number of possible arrangements of the word 'BASSOON' if repeated letters are treated as identical?

    <p>1,260</p> Signup and view all the answers

    What is the probability that the number plate starts with 'Y' and ends with an odd digit?

    <p>0.216</p> Signup and view all the answers

    How many arrangements are there if the word 'BASSOON' starts and ends with the letter 'S'?

    <p>60</p> Signup and view all the answers

    What is the total number of possible number plates?

    <p>926,100</p> Signup and view all the answers

    What is the probability that the word 'BASSOON' starts and ends with the same letter?

    <p>0.0952</p> Signup and view all the answers

    What is the general formula for calculating the probability of an event E occurring?

    <p>P(E) = n(E) / n(S)</p> Signup and view all the answers

    What is the number of options for the first and second digits in a number plate?

    <p>20</p> Signup and view all the answers

    A password consists of 5 digits and can be repeated. How many possible passwords are there?

    <p>10^5</p> Signup and view all the answers

    What is the probability that a number plate starts with 'Y' and ends with an odd digit?

    <p>0.216</p> Signup and view all the answers

    A license plate consists of 3 letters (excluding vowels and 'Q') followed by 3 digits. What is the total number of possible license plates?

    <p>151,200,000</p> Signup and view all the answers

    How many arrangements are there if the word 'BASSOON' starts and ends with the letter 'O'?

    <p>60</p> Signup and view all the answers

    What is the probability that a 4-digit PIN contains at least one even digit if digits can be repeated?

    <p>0.84375</p> Signup and view all the answers

    What is the total number of possible arrangements of the word 'BASSOON' if repeated letters are ignored?

    <p>1,260</p> Signup and view all the answers

    A combination lock consists of 3 numbers (0-9) and can be repeated. What is the probability that the lock opens with a combination that contains at least one 0?

    <p>0.729</p> Signup and view all the answers

    A lottery drawing consists of 4 numbers (1-40) and cannot be repeated. What is the total number of possible lottery drawings?

    <p>40 * 39 * 38 * 37</p> Signup and view all the answers

    What is the probability that the word 'BASSOON' starts and ends with the same letter?

    <p>0.0952</p> Signup and view all the answers

    How many options are there for the last digit of a number plate?

    <p>5</p> Signup and view all the answers

    What is the probability that a randomly selected car license plate starts with the letter 'K'?

    <p>1/20</p> Signup and view all the answers

    A password consists of 6 characters (A-Z, 0-9) and can be repeated. What is the probability that the password contains at least one digit?

    <p>0.984</p> Signup and view all the answers

    What is the number of possible arrangements of the word 'BASSOON' if repeated letters are treated as distinct?

    <p>5040</p> Signup and view all the answers

    A license plate consists of 3 letters (excluding vowels and 'Q') followed by 3 digits. What is the probability that the license plate starts with 'Y' and ends with an odd digit?

    <p>0.216</p> Signup and view all the answers

    What is the total number of possible arrangements of the word 'BASSOON' if the word starts and ends with 'S' or 'O'?

    <p>240</p> Signup and view all the answers

    What is the total number of possible car number plates?

    <p>926,100</p> Signup and view all the answers

    What is the probability that a randomly selected word arrangement of 'BASSOON' starts and ends with the same letter, given that the word arrangement is chosen uniformly at random?

    <p>0.0952</p> Signup and view all the answers

    If a 3-letter word arrangement is chosen uniformly at random from the 7 distinct letters of 'BASSOON', what is the probability that the first and last letters are the same?

    <p>1/7</p> Signup and view all the answers

    If a PIN consists of 5 digits and digits can be repeated, what is the total number of possible PINs?

    <p>100,000,000</p> Signup and view all the answers

    What is the probability that a PIN of 4 digits contains at least one even digit if digits cannot be repeated?

    <p>0.625</p> Signup and view all the answers

    A car number plate consists of 3 letters (excluding vowels and 'Q') followed by 3 digits. What is the probability that the number plate starts with the letter 'B' and ends with an even digit?

    <p>0.005</p> Signup and view all the answers

    If a PIN consists of 6 digits and digits can be repeated, what is the probability that the PIN contains at least two 8's?

    <p>0.0539</p> Signup and view all the answers

    A car number plate consists of 3 letters (excluding vowels and 'Q') followed by 3 digits. What is the probability that the number plate contains at least one letter 'T' and at least one digit '3'?

    <p>0.2727</p> Signup and view all the answers

    If a PIN consists of 5 digits and digits cannot be repeated, what is the probability that the PIN contains at least one 8 and at least one 9?

    <p>0.4286</p> Signup and view all the answers

    A car number plate consists of 3 letters (excluding vowels and 'Q') followed by 3 digits. What is the probability that the number plate starts with the letter 'A' and ends with an odd digit?

    <p>0.05</p> Signup and view all the answers

    If a PIN consists of 4 digits and digits can be repeated, what is the probability that the PIN contains at least three 8's?

    <p>0.0081</p> Signup and view all the answers

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