An actress has a probability of getting offered a job after a try-out of 0.04. She plans to keep trying out for new jobs until she gets offered. Assume outcomes of try-outs are independent.
Find the probability she will need to attend more than 6 try-outs.
To find the probability that the actress will need to attend more than 6 try-outs, we need to calculate the probability of her not being offered a job in the first 6 try-outs and then subtract it from 1.
Since the outcomes of try-outs are independent, the probability of not being offered a job in a single try-out is given by (1 - 0.04) = 0.96.
Now we need to calculate the probability of not being offered a job in the first six try-outs. Since each try-out is independent, we multiply the probabilities together:
Probability of not being offered a job in the first 6 try-outs = (0.96)^6 = 0.7350918906.
Finally, we subtract this probability from 1 to find the probability that she will need to attend more than 6 try-outs:
Probability of attending more than 6 try-outs = 1 - 0.7350918906 ≈ 0.2649081094.
Therefore, the probability she will need to attend more than 6 try-outs is approximately 0.2649, or 26.49%.