In Yahtzee, 5 dice are rolled. Find the probability of rolling at least one 6.
Answer: 4651/7776
Thanks for any help
Prob(six) = 1/6
prob(not six) = 5/6
Prob(not six in all 5 throws) = C(5,5) (5/6)^5
= 3125/7776
So prob(at least 1 six) = 1 - 3125/7776
= 4651/7776
rolling five at a time is the same as five individual rolls
... they are independent events
at least one means NOT none
for one die ... p(not 6) = 5/6
for five dice ... p(not 6) = (5/6)^5
at least one ... 1 - [(5/6)^5]
To find the probability of rolling at least one 6 in Yahtzee with 5 dice, you can use the compliment rule.
Step 1: Find the probability of not rolling a 6 on one die.
Since there are 6 possible outcomes on one die (numbers 1 to 6), the probability of not rolling a 6 is 5/6.
Step 2: Calculate the probability of not rolling a 6 on all 5 dice.
Since each die is rolled independently, the probability of not rolling a 6 on all 5 dice is (5/6)^5.
Step 3: Calculate the probability of rolling at least one 6.
The compliment rule states that the probability of an event occurring is equal to 1 minus the probability of the event not occurring. Therefore, the probability of rolling at least one 6 is 1 - (5/6)^5.
Now let's calculate it:
Step 4: Simplify the expression.
1 - (5/6)^5 = 1 - 3125/7776 = (7776/7776) - (3125/7776) = 4651/7776.
So, the probability of rolling at least one 6 in Yahtzee with 5 dice is 4651/7776.
To find the probability of rolling at least one 6 in Yahtzee, we first need to calculate the total number of possible outcomes when rolling 5 dice. Each die has 6 possible outcomes (numbers 1 to 6), so the total number of possible outcomes when rolling 5 dice is 6^5 = 7776.
Next, we want to determine the number of outcomes that includes at least one 6. To find this, we can use the concept of complementary probability. The complementary probability of an event A is equal to 1 minus the probability of the event not occurring (A'). In this case, the event A is rolling at least one 6, and the complementary event A' is rolling no 6s.
To calculate the number of outcomes with no 6s, we need to consider that each die has 5 possible outcomes (numbers 1 to 5) that are not 6. Therefore, the total number of outcomes with no 6s when rolling 5 dice is 5^5 = 3125.
Now, we can calculate the probability of rolling at least one 6 by using the formula:
P(A) = 1 - P(A')
P(A) = 1 - (number of outcomes with no 6s / total number of possible outcomes)
P(A) = 1 - (3125 / 7776)
P(A) = (7776 - 3125) / 7776
P(A) = 4651 / 7776
Therefore, the probability of rolling at least one 6 in Yahtzee is 4651/7776.