GMATMadeEasy wrote:If there are 2 freshman, 2 sophomores, 2 juniors and 2 seniors. If a 2-person group must consist of persons from different classes, what is the probability of choosing a group consisting of one freshman and one sophomore?
§ Ways to choose a freshman/sophomore group: 2C1 *2C1 = 4
What is the best way to choose total number of groups ?
Good = Total - Bad
Total possible groups = 8C2 = 28
Bad groups = 4 (2 freshman, 2 sophomores, 2 juniors, or 2 seniors)
Good = 28 - 4 = 24
So we can form 24 2-person groups if we have to choose from different classes.
As you noted, a good outcome is combining 1 freshman (giving us 2 choices) and 1 sophomore (giving us 2 choices): 2*2 = 4.
P(1 freshman and 1 sophomore) = 4/24 = 1/6.
Another approach:
P(freshman or sophomore on the 1st pick): 4/8
For the 2nd pick, we can't choose from the same class chosen on the 1st pick, so we'll have only 6 people left to choose from. Of these 6, 2 will be from the freshman or sophomore class. Thus:
P(freshman or sophomore on the 2nd pick): 2/6
Since we need both events to happen, we multiply the fractions:
4/8 * 2/6 = 1/6.
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