Question

1. If you make random guesses for 7 multiple choice questions (each with 5 possible answers), what is the probability of getting at least one answer correct?

2. Find the probability that two randomly selected people were both born on Christmas day.(Ignore leap years)

3. Find the probability that two randomly selected people were born on the same day. (Ignore leap years)

4. You are trying to guess a 6 digit password using 0 through 9. Repetitions of digits are allowed. What is the probability of guessing the correct password on a first try?

5. Assume that you have a calculator that has a working rate of 97%. You want to use 2 calculators that have the same working rate to ensure that you have a working calculator. What is the probability that you will have at least one working calculator?

Answer 1

1)as probabiltiy of getting an answer wrong =4/5 (as 4 wrong answer out of 5)

P(getting at least one answer correct)=1-P(all wrong answers) =1-(4/5)⁷ =0.7903

2)probability that two randomly selected people were both born on Christmas day.

=P(fisrt on Christmas day)*P(second on Christmas day)=(1/365)*(1/365)=0.0000075

3)

probability that two randomly selected people were born on the same day=P(first can born on any of 365 days)*P(second has onl;y 1 choice as of first one to have birthday)=(365/365)*(1/365)

=1/365 =0.00274

4)

total number of 6 digit password =N(for each digit 10 options are there) =10⁶

hence P(f guessing the correct password on a first try) =1/10⁶ =0.000001

5)probability that you will have at least one working calculator =1-P(both are not working)

=1-(1-0.97)² =0.9991