1A. A factory produces three types of light bulbs: LED, CFL,…

1A. A factory produces three types of light bulbs: LED, CFL, and incandescent. The production probabilities for these types of light bulbs are as follows: 50% are LED, 30% are CFL, and 20% are  incandescent. The probability of a light bulb being defective given its type is: 2% for LED, 5% for CFL and 8% for incandescent. If a randomly selected light bulb from the factory’s production line is found to be defective, what is the probability that the defective light bulb is an LED? Please show all your work, first write the formulas you are using then plug in the given value.

  3B. The probability that a bit transmitted through a digit…

  3B. The probability that a bit transmitted through a digital transmission channel is received in error is 0.1. Transmissions are independent events. What distribution you are using? Write the formula for the following questions then calculate. (a) What is the probability that the first four bits are transmitted correctly, and the fifth bit is in error? (b) The mean number of transmissions until the first error is (c) The standard deviation of the number of transmissions before the first error is  

2A. In a school, 250 students were surveyed about their part…

2A. In a school, 250 students were surveyed about their participation in extracurricular activities. The survey results showed: 140 students are in the drama club. 110 students are in the music club. 60 students are in both the drama club and the music club. (a) How many students are only in the drama club? (b) How many students are only in the music club? (c) How many students are not in either the drama club or the music club? Show all your work don’t just write the answers.