Dr. Owino needs two students to help him with a science demonstration for his class of 18 girls and 12 boys. He randomly chooses one student who comes in front of classroom. He then chooses a second student from those still seated. What is the probability that both students chosen are girls?
Well, if Dr. Owino randomly chooses the students, then let's assume he has a pair of magic dice that only have two sides: one for girls and one for boys. Now, let's roll those dice and see what happens.
First roll: The probability of rolling the girl side is 18 out of 30, because there are 18 girls out of 30 students in total.
Second roll: After the first student is chosen and already standing in front of the class, the probability of rolling the girl side decreases slightly to 17 out of 29, because there is one less girl available to choose from.
To find the probability of both students being girls, we need to multiply the probabilities of each roll:
(P(girl on first roll)) * (P(girl on second roll)) = (18/30) * (17/29) ≈ 0.3269
So, the probability that both students chosen are girls is approximately 0.3269, or about 32.69%.
To find the probability that both students chosen are girls, we can use the concept of conditional probability. Given that the first student chosen is a girl, the number of girls remaining in the class is 17 (since one girl is already chosen) and the total number of remaining students is 29 (18 girls and 12 boys).
The probability of choosing a second girl, given that the first student chosen is a girl, can be calculated as:
Probability of second student being a girl = (Number of remaining girls) / (Number of remaining students)
= 17 / 29
Therefore, the probability that both students chosen are girls is 17/29.
To find the probability that both students chosen are girls, we need to determine the total number of possible outcomes and the number of favorable outcomes.
Total number of possible outcomes:
Dr. Owino randomly selects one student from the class of 18 girls and 12 boys. There are 30 students in total. So, the number of possible outcomes for the first selection is 30.
For the second selection, after one student has already been chosen, there are now 29 students remaining.
Number of favorable outcomes:
Since Dr. Owino needs two students who are both girls, there are 18 girls to choose from for the first selection and 17 girls to choose from for the second selection.
To calculate the probability, we divide the number of favorable outcomes by the total number of possible outcomes:
Probability = (number of favorable outcomes) / (total number of possible outcomes)
= (18/30) * (17/29)
Simplifying this expression gives:
Probability = 306 / 870
= 0.352
Therefore, the probability that both students chosen are girls is approximately 0.352, or 35.2%.