Question

Which of the values below is the probability that of three randomly selected people, none of them were born on a Monday?
.003
.63
.73
.86
1.0

Answer 1

Assuming the probability of being born on any given day of the week is the same (so that it isn't, for whatever reason, more likely to be born on Tuesdays than Fridays), we can say that the probability of being born on a Monday is 1/7. Thus, the probability of being born on any day BUT a Monday is 6/7 (there are six other days in the week).

Each person's birthday is independent of another's, so the probability of the three of them NOT being born on a Monday is the same as the probability of:

Person 1 not born on Monday AND Person 2 not born on Monday AND Person 3 not born on Monday.

This is equivalent to:
\[(\frac{ 6 }{ 7 })(\frac{ 6 }{ 7 })(\frac{ 6 }{ 7 })=(\frac{ 6 }{ 7 })^3\]
\[(\frac{ 6 }{ 7 })^3=0.629737609\approx0.623\]

Answer 2

Sorry... that last one should be 0.63...

Answer 3

Thanks @DeoxNA