ACT Preparation / Unit 15 ACT 1425 worked example, 60 to 90 seconds
Or, With an Overlap
The idea
An or-probability is found in three steps. First, decide whether the two events can happen together. Second, if they cannot, add their probabilities. Third, if they can, add them and subtract the probability of both, so that the overlap is counted once; a two-way table or a Venn diagram shows the overlap directly.
In practice
Worked example: in a club of 40, 22 play soccer, 15 play tennis, and 7 play both. P(soccer or tennis) = 22/40 + 15/40 − 7/40 = 30/40 = 3/4. The other 40 − 30 = 10 members play neither. By contrast, a die roll that is even or a 5 has no overlap: 3/6 + 1/6 = 4/6.
Where people slip
Without the subtraction, 37 of 40 would seem to play, because the 7 who play both would be counted twice.
Your place on the trail
Every lesson rests on earlier ones and opens later ones. Tap any to jump.
Unlocks
- Nothing yet depends on this.
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