Question

1. A 4-digit number is created from the numbers {1,2,3,4,5,6}. How many ways can the digits be chosen so that the number is more than 1500?

2. An applied statistics class contains 30% sophomores, 40% juniors, and the rest seniors. If 40% of the sophomores, 20% of the juniors, and 10% of the seniors will fail, what is the probability a randomly selected student in the class will fail?

3. A coin is flipped 10 times or until 3 heads are flipped. Would this experiment be a Bernoulli process? Explain.

Answer 1

1)without repetition"

number of ways =N(first number is 1 and 2nd number is 5 or more}+N(first number is 2 or more)

=1*2*4*3+5*5*4*3 =324

with repetition"

number of ways =N(first number is 1 and 2nd number is 5 or more}+N(first number is 2 or more)

=1*2*6*6+5*6*6*6 =1152

2)

P(fail)=P( sophomores )*P(fail| sophomores )+P( Junior )*P(fail junior )+P( senior )*P(fail| senior)

=0.3*0.4+0.4*0.2+0.3*0.1

=0.23

3)

No, since here number of trails are not fixed and continues till the desired outcome is achieved or till 10 flips