Question

.1. There are 30 people who have applied for a job. 3 of them are going to be hired. How many different sets of 3 people are possible? 

2. A weighted coin has probability 0.7 of getting heads, and 0.3 of getting a tails. If the coin is tossed 6 times, what is the probability of getting at least 4 heads? What is the probability of getting less than 4 heads? 

3. Given the following data set: 1,1,1,2,2,3,3,4,5,6. 

a. Find the probability distribution of X where X is the relative frequency of each number in the data set. 

b. Find the expected value of X. 

Answer 1

n= 30, x= 3 The different sets of 3 people are possible = c = 3 c = 4060 :: 4060 different sets are possible with 3 people Probability of getting head = 0.7, Probability of getting a tail = 0.3 and n = 6 The probability of getting at least 4 heads: P/X2x) = ( )* (p)** (1 – p)n-* P(X2 4) = P (X = 4) + P (X = 5) + P (X = 6) = (%)*(0.7)* + (0.3)2 + (3) + (0.7)5 + (0.3)2 + () *(0.7)6+ (0.3)” = 0.3241 +0.3025 + 0.1177 = 0.7443 : The probability of getting at least 4 heads = 0.7443 Probability of getting less than 4 heads: P(X < 4) = 1-P (X 24) = 1-0.7443 = 0.2558 ... Probability of getting less than 4 heads = 0.2558

1,1,1 3) Given data set: 1,1,1,2,2,3,3,4,5,6. Data Frequency X (Relative Frequency) 0.3 2,2 2 3,3 2 4 1 0.1 0.1 a. The probability distribution of X: X P(X) 0.3 1/6 0.2 2/6 0.1 3/6 b. The expected value of X: E (X) = 0.3*4 + 0.243 +0.142 = 0.05+0.067+0.05 E (X) = 0.167 [Note: we are not allowed to solve many questions at a time, please post the remaining questions separately ]