If 5 juniors and 4 seniors apply for a job at a school which has 2 openings, what is the probability that 1 junior and 1 senior will be randomly chosen for the job.
To find the probability of 1 junior and 1 senior being randomly chosen for the job out of the total applicants, we need to calculate two probabilities: the probability of selecting 1 junior and 1 senior.
Step 1: Calculate the probability of selecting 1 junior.
There are 5 juniors out of a total of 9 applicants. Therefore, the probability of selecting 1 junior can be calculated as 5/9.
Step 2: Calculate the probability of selecting 1 senior.
There are 4 seniors out of a total of 9 applicants. Therefore, the probability of selecting 1 senior can be calculated as 4/9.
Step 3: Multiply the probabilities.
Since we want both events (1 junior and 1 senior being chosen) to occur, we need to multiply the probabilities.
Probability of selecting 1 junior and 1 senior = (5/9) * (4/9)
Step 4: Simplify the fraction if necessary.
To simplify the fraction, multiply the numerator and denominator by the common factors, if any.
Probability of selecting 1 junior and 1 senior = (5 * 4) / (9 * 9)
= 20 / 81
Therefore, the probability that 1 junior and 1 senior will be randomly chosen for the job is 20/81.