On an entrance examination for Fairlywell College, % of the students pass the mathematics sections, 4/5 pass the English, and 2/3 pass both sections. Find the probability of each event A student will pass mathematics OR English a student will pass mathematics, given that he or she passed English A student will pass English, given that he or she passed mathematics.

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### Entrance Examination Probability Problem

In an entrance examination for Fairlywell College, the following statistics are observed:

- ¾ of the students pass the mathematics section.
- 4/5 pass the English section.
- 2/3 pass both sections.

Determine the probability for each of the following events:

1. A student will pass either mathematics **OR** English:

   \_\_\_\_\_\_\_

2. A student will pass mathematics, given that he or she passed English:

   \_\_\_\_\_\_\_

3. A student will pass English, given that he or she passed mathematics:

   \_\_\_\_\_\_\_

**Note:** These probabilities involve understanding and applying principles of conditional probability and union of events.
Transcribed Image Text:### Entrance Examination Probability Problem In an entrance examination for Fairlywell College, the following statistics are observed: - ¾ of the students pass the mathematics section. - 4/5 pass the English section. - 2/3 pass both sections. Determine the probability for each of the following events: 1. A student will pass either mathematics **OR** English: \_\_\_\_\_\_\_ 2. A student will pass mathematics, given that he or she passed English: \_\_\_\_\_\_\_ 3. A student will pass English, given that he or she passed mathematics: \_\_\_\_\_\_\_ **Note:** These probabilities involve understanding and applying principles of conditional probability and union of events.
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