In a certain liberal arts college with about 10,000 students, 40% are males. If two students from this college are selected at random, what is the probability that they are of the same gender? 0.96 0.52 0.48 0.36 0.16
Question
In a certain liberal arts college with about 10,000 students, 40% are males. If two students from this college are selected at random, what is the probability that they are of the same gender? 0.96 0.52 0.48 0.36 0.16
Solution
To solve this problem, we need to calculate the probability of selecting two males and the probability of selecting two females, and then add these two probabilities together.
- Calculate the probability of selecting two males:
The probability of selecting one male is 40%, or 0.4. Since we're selecting two students, we need to multiply this probability by itself: 0.4 * 0.4 = 0.16.
- Calculate the probability of selecting two females:
Since 40% of the students are males, that means 60% are females. The probability of selecting one female is 0.6. Again, since we're selecting two students, we need to multiply this probability by itself: 0.6 * 0.6 = 0.36.
- Add the two probabilities together:
0.16 (probability of two males) + 0.36 (probability of two females) = 0.52.
So, the probability that two students selected at random are of the same gender is 0.52.
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