1. If everyone in a group of 4 people rolls a 6 sided die, what is
the probability that at least one person gets a 6?
1 - P(no one get's a 6) =
1 - (5/6)(5/6)(5/6)(5/6) or 1 - (5/6)4 ≈
.52 = 52%
2. If everyone in a group of 4 people rolls a 6 sided die, what is
the probability that at least one person gets a 2?
This one has exactly the same answer as
the last one. It doesn't matter what number on the die you are
trying for, it has the same probability of turning up. The 5/6 in
the calculation means that 5/6 of the time you don't get 2: there's one 2 on the die, and five other numbers, so there's a 5/6
chance that you don't roll 2.
3. If I roll a 6-sided die 4 times, what is the probability that I
get at least one 2?
This one has exactly the same answer as
the last one--it doesn't matter whether you roll 4 dice once, or 1 die
4 times, the probabilities are the same.
4. If I roll a 6- sided die 5 times, what is the probability that I
don't get a 2 on any of the rolls?
(5/6)(5/6)(5/6)(5/6)(5/6) or (5/6)5
≈
.40 = 40%
You don't subtract from 1, because this is asking what the probability
is that you get no 2's (this is the simpler problem), rather than the
probability that you get at least one 2.
The multiplication goes (prob of not getting 2 on the first die)(prob
of not 2 on second die)(prob not 2 on 3rd die)(prob of not 2 on 4th
die)(prob of not 2 on 5th die)
5. If I roll a 12-sided die 4 times, what is the probability that I
get a 3 at least once
1 - P(no 3's) =
1 - (11/12)(11/12)(11/12)(11/12) or 1 - (11/12)4 ≈
.29 = 29%
6. In a group of 8 people, what is the probability that someone has
a birthday in January?
1 - P(no January's) =
1 - (11/12)(11/12)(11/12)(11/12)(11/12)(11/12)(11/12)(11/12) or 1 -
(11/12)8 ≈
.50 = 50%
7. If I roll a 10-sided die 5 times, what's the probability that I
don't get a 4 on any of the rolls?
(9/10)(9/10)(9/10)(9/10)(9/10) or (9/10)5
≈
.59 = 59%
8. If I roll a 6-sided die 8 times, what is the probability that I
get at least one 4?
1 - P(no 4's) =
1 - (5/6)(5/6)(5/6)(5/6)(5/6)(5/6)(5/6)(5/6) or 1 - (5/6)8 ≈
.77 = 77%
9. If everyone in a group of 5 people rolls a 20 sided die, what is
the probability that someone will get a 1?
1 - P(no 1's) =
1 - (19/20)(19/20)(19/20)(19/20)(19/20) or 1 - (19/20)5 ≈
.23 = 23%