Answer:
P = 0.00000751
the probability that 3 randomly selected people all have the same birthday is 0.00000751
Explanation:
the probability that 3 randomly selected people all have the same birthday P;
P = P1 × P2 × P3 ........1
For the first person, since there is no specified date, he can have any of the 365 days of the year as his birthday. the probability P1 is;
P1 = 365/365 = 1
For the second person, he must have the same birthday as the first. The probability P2 is;
P2 = 1/365
The third person must also have the same birthday as the other two. The probability P3 is;
P3 = 1/365
Substituting the values into equation 1;
P = 1 × 1/365 × 1/365
P = 0.0000075060987051
To eight decimal places;
P = 0.00000751
the probability that 3 randomly selected people all have the same birthday is 0.00000751