Probabilty problem

**Phodot** · October 21st 2010, 06:14 PM

Hello forum :]

I am in need of some help on this probability problem.

The probability of being born on a Friday the 13th is 1/214. Assume the days of people's birth are independent of each other.

(a) You meet two new friends; what is the probability that both new friends were born on a Friday the 13th?

I got this one, just use the multiplication rule so: (1/214)(1/214) = 1/45796

(b) You meet 31 new friends; what is the probability that at least one of these new friends was born on a Friday the 13th?

I cant figure this out. If they were disjoint then I could just use the addition rule, but they aren't so I am very confused.

Any help will be greatly appreciated.

**Soroban** · October 21st 2010, 08:42 PM

Hello, Phodot!

The probability of being born on a Friday the 13th is 1/214.
Assume the days of people's birth are independent of each other.

(a) You meet two new friends. What is the probability that
both new friends were born on a Friday the 13th?

I got this one, just use the multiplication rule so: $(\frac{1}{214})(\frac{1}{214}) \:=\: \frac{1}{45,\!796}$ . Right!

(b) You meet 31 new friends; what is the probability that
at least one of these new friends was born on a Friday the 13th?

The opposite of "at least one" is "none."

The probability that none were borh on Friday the 13th is: . $(\frac{213}{214})^{31}$

Therefore: . $P(\text{at least one Friday the 13th}) \;=\;1 - \left(\frac{213}{214}\right)^{31} \;\approx\;13.5\%$

**Phodot** · October 21st 2010, 09:04 PM

Thank you very much :]

Thread: Probabilty problem

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