NEED HELPS PLEASE

STATISTICS AND PROBABILITY

- Always define the random variable x first before using it in your solution.

- If the final answer exceeds five decimal places, round it off to four places only.

1. The probability that a student is accepted to a prestigious college is 0.3. If 5 students apply to the college, what is the probability that at most 2 are accepted?

2. An agent sells life insurance policies to five equally aged, healthy people. According to recent data, the probability of a person living in these conditions for 30 years or more is 2/3. Calculate the probability that after 30 years:

a. all five people are still living.

b. at least three people are still living.

c. exactly two people are still living.

3. We flip a coin 10 times. Find the probability that 6 heads are obtained.

4. A coin is tossed four times. Calculate the probability of obtaining more heads than tails.

5. If from six to seven in the evening one telephone line in every five is engaged in a conversation: what is the probability that when 10 telephone numbers are chosen at random, only two are in use?

6. The probability of a man hitting the target at a shooting range is 1/4. If he shoots 10 times: a. What is the probability that he hits the target exactly three times? b. What is the probability that he hits the target at least once?

7.There are 10 red and 20 blue balls in a box. A ball is chosen at random and it is noted whether it is red. The process repeats, returning the ball 10 times. Calculate the expected value and the standard deviation of this game.

8. A pharmaceutical lab states that a drug causes negative side effects in 3 of every 100 patients. To confirm this affirmation, another laboratory chooses 5 people at random who have consumed the drug. What is the probability of the following events?

a. None of the five patients experience side effects

b. At least two experience side effects.

c. What is the average number of patients that the laboratory should expect to experience side effects if they choose 100 patients at random?

9. When looking at a person's eye color, it turns out that 1% of people in the world has green eyes. Consider a group of 20 people. Find the probability that no one has green eyes.

10. Approximately 10% of all people are left-handed ("11 little-known facts," 2013). Consider a grouping of fifteen people. Find the probability that :

a. none are left-handed

b. seven are left-handed

c. at least two are left-handed (use the complement rule)