Question

Probability Theory and Mathematical statistics Final examination Variant 3 Part 1. Random Events 1. The probability of some event in each experiment is 0.009. Find the probability of exactly 3 successes during 340 experiments. 2. A square has a side of 21 cm and has a circle with radius equal to 7 cm within t. Find the probability of a dart hitting the circle if it hits the square. 3.75% of people attend their primary care physician regularly: 28% of those people have no health problems crop up during the following year. Out of the 25% of people who don't see their doctor regularly, only 18% have no health issues during the following year what is the probability a random person will have no health problems in the following year? Part 2. Random Variables

Answer 1

1) The probability of success is 0.009 The sample size is 340. Consider Xis the random variable that represents the number of success. The random variable X follows binomial distribution because the probability of success is fixed for every experiment and the number of experiments is independent Calculate the probability of exactly 3 success during 340 experiments. 72 30.009) (1-0.009)*- 340 (0.000000729)(0.047514) -(6492980) (0.000000729) (0.047514) 0.2249