Q1. There are 7 days in a week. If there are 3 friends in a hangout, what is the probability that all of them have birthdays on the same weekday?
Q2. There are 50 balls in a box marked by the positive integers from 1 to 50. If you randomly pick 8 balls, what is the probability that you get 3 numbers less than 21, 2 numbers less or equal to 36 and greater than 24, 3 numbers greater than 42? (Round your answer upto 4 decimal places)
Answers
Answer:
Q1.Let’s find the probability that the birthdays of all 7 people falling on 7 different days of the week:
The first person has a 100% chance of a unique day of the week (of course) = 1
The second has a (1 – 1/7) chance = 6/7
The third has a (1 – 2/7) chance (all but 2 days) = 5/7
The fourth has a (1 – 3/7) (all but 3 days) = 4/7
The fifth has a (1 – 4/7) chance = 3/7
The sixth has a (1 – 5/7) chance = 2/7
The seventh has a (1 – 6/7) = 1/7
Probability (all have birthdays of different days) = 1*(6/7)*(5/7)*(4/7)*(3/7)*(2/7)*(1/7) = (2*3*4*5*6) / (7^6) = 720/7^6 = 720/ 117649 = 0.006119899 approx.
So there is an approximately 0.612% chance that all 7 have birthdays on 7 different days of the week.
So, the probability that 2 or more have birthdays of the same day
= (100 - 0.612)% approx.
= 99.39% approx.
Step-by-step explanation:
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