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The probability of failing an examination is 0.25. a) What is the probability of passing the examination? b) If 900 students sat for the examination, how many of them passed the examination?

Mathematics

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Answers

2 parts
a
0.75
b
675

Step-by-step solution

4 steps

Here's how to solve this probability problem:

Part a· 2 steps

What is the probability of passing the examination?

  1. Understand that the probability of an event happening and the probability of it not happening sum to 1.

    P(passing)+P(failing)=1P(\text{passing}) + P(\text{failing}) = 1
  2. Substitute the given probability of failing and solve for the probability of passing.

    P(passing)+0.25=1P(\text{passing}) + 0.25 = 1 P(passing)=1−0.25P(\text{passing}) = 1 - 0.25 P(passing)=0.75P(\text{passing}) = 0.75

    The probability of passing the examination is 0.75\boxed{0.75}.

Part b675

If 900 students sat for the examination, how many of them passed the examination?

  1. Use the probability of passing found in part (a) and the total number of students.

    Number of students who passed = Total number of students ×\times Probability of passing

  2. Calculate the number of students who passed.

    Number of students who passed=900×0.75\text{Number of students who passed} = 900 \times 0.75 Number of students who passed=675\text{Number of students who passed} = 675

    The number of students who passed the examination is 675\boxed{675}.

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