# Question: (2 points) Consider the experiment where a fair coin is flipped 3 times. Let F represent the event that Heads come up at most 2 in the three flips. Find P(F) 2. 3. Suzan grabs five marbles at random from a bag containing four red marbles, three green ones, two white ones and one purple one. What is the probabilities of the following events expressing each as a fraction in the lowest term a. She has at least 2 green ones. (2 points) b. She does not have all the red ones. (2 points)

Transcribed text From Image:(2 points) Consider the experiment where a fair coin is flipped 3 times. Let F represent the event that Heads come up at most 2 in the three flips. Find P(F) 2. 3. Suzan grabs five marbles at random from a bag containing four red marbles, three green ones, two white ones and one purple one. What is the probabilities of the following events expressing each as a fraction in the lowest term a. She has at least 2 green ones. (2 points) b. She does not have all the red ones. (2 points)

Answer:

2) Given data

A coin is tossed three times

so the sample space ={HHH ,HHT ,HTT, TTH, HTH, THT, THH ,TTT } =8

events in which head comes at most 2 times (F) ={HHT ,HTT ,TTH, HTH, THT ,THH, TTT}=7

3)given data

Green marbel =4

red marbel =3

white marbel =2

purple marbel=1

total number of marbel =10

number of times marbel taken (n)=5

a) we have to find the probablity of getting at least 2 red marbel

let probablity of getting a red marble =R

here sucess getting a red marbel

so probablity of sucess (p)=4/10=0.4

probablity of failure (q)=1-p =1-0.4=0.6

now from the formula of binomial approximation

b) now we have to find the probablity of getting 4 red ball at most

let probablity of getting a red marble =R