There are 20 students in a class. Six of them have blue eyes and nine have brown eyes. You were asked to choose 2 students without replacement. What is the probability of choosing an student with blue eyes followed by a student with brown eyes?
Step 1
initially there are 20 students of which 6 have blue eyes.
Probability of choosing the first with blue eyes is 6/20.
Step 2
There are then 19 students left of which 9 have brown eyes.
Then the probability of choosing a brown eyed student is 9/19.
Since it is a two-step experiment, the probability of succeeding both steps is the product of the two probabilities:
6/20*9/19=27/190
To calculate the probability of choosing a student with blue eyes followed by a student with brown eyes, we need to consider the total number of possible outcomes and the number of favorable outcomes.
Step 1: Calculate the total number of possible outcomes.
When choosing two students without replacement, the total number of possible outcomes can be calculated using the combination formula:
nCr = n! / ((n - r)! * r!)
In this case, there are 20 students in the class, so n = 20. We are choosing 2 students, so r = 2.
Total number of possible outcomes = 20C2
= 20! / ((20 - 2)! * 2!)
= (20 * 19) / (2 * 1)
= 380 / 2
= 190
Therefore, there are 190 total possible outcomes when choosing 2 students from the class.
Step 2: Calculate the number of favorable outcomes.
To calculate the favorable outcomes, we need to consider the number of ways to choose one student with blue eyes followed by one student with brown eyes.
Number of favorable outcomes = (Number of ways to choose one student with blue eyes) * (Number of ways to choose one student with brown eyes)
Number of ways to choose one student with blue eyes = 6 (since there are 6 students with blue eyes)
Number of ways to choose one student with brown eyes = 9 (since there are 9 students with brown eyes)
Number of favorable outcomes = 6 * 9
= 54
Step 3: Calculate the probability.
To calculate the probability, divide the number of favorable outcomes by the total number of possible outcomes.
Probability = Number of favorable outcomes / Total number of possible outcomes
= 54 / 190
≈ 0.2842 (rounded to four decimal places)
Therefore, the probability of choosing a student with blue eyes followed by a student with brown eyes is approximately 0.2842.
To find the probability of choosing a student with blue eyes followed by a student with brown eyes, we need to calculate the probability of each event individually and then multiply them together.
First, let's find the probability of choosing a student with blue eyes as the first pick. Since there are 6 students with blue eyes out of the total 20 students, the probability of picking a student with blue eyes on the first pick is 6/20.
Next, in order to find the probability of choosing a student with brown eyes as the second pick, we need to consider that the first student selected has already been removed from the pool. Therefore, there are now only 19 students left and 9 of them have brown eyes. Thus, the probability of picking a student with brown eyes as the second pick is 9/19.
To find the final probability, we need to multiply the probability of the first event (picking a student with blue eyes) by the probability of the second event (picking a student with brown eyes).
Therefore, the probability of choosing a student with blue eyes followed by a student with brown eyes is (6/20) * (9/19), which simplifies to 27/190 or approximately 0.1421.