math

posted by .

A six-sided die (with numbers 1 through 6) and an eight-sided die (with numbers 1 through 8) are rolled. What is the probability that there is exactly one 6 showing? Express your answer as a common fraction.

  • math -

    For all probabilities, multiply individual probabilities. For either-or probabilities, add.

    (1/6 * 7/8) + (5/6 * 1/8) = ?

  • math -

    2/5

  • math -

    1/4

  • math -

    There are 2 cases: the 6 is rolled either on the 6 or 8 sided die. Therefore, we have ((1/6)(7/8))+((5/6)(1/8))=1/4.

  • math -

    We proceed using casework. If there is exactly one 6 showing, then the 6 must be on the six-sided die or the eight-sided die (but not both).

    Case 1: 6 on the 6-sided die and not on the 8-sided die
    The probability of getting a 6 with the six-sided die is 1/6, and the probability of not rolling a 6 with the eight-sided die is 7/8. We multiply these to build up to the full case: $\dfrac16 \cdot \dfrac78 = \dfrac7{48}$.

    Case 2: 6 not on the 6-sided die and on the 8-sided die
    The probability of not getting a 6 with the six-sided die is 5/6, and the probability of rolling a 6 with the eight-sided die is 1/8. Together, these have a probability of $\dfrac56 \cdot \dfrac18 = \dfrac5{48}$.

    Now we add the probabilities from the separate cases. The probability that there is exactly one 6 is
    \[ \frac{7}{48} + \frac{5}{48} = \frac{12}{48} = \boxed{\frac{1}{4}}.\]

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. math

    If a standard six-sided die is rolled twice, what is the probability that the result of the second roll is not less than the result of the first roll?
  2. pre-algebra B

    Milli tosses a coin and a six-sided die.The numbers on the die are 1 through 6. What is the probability that Milli will toss a tail and roll an odd number?
  3. math

    A fair, six-sided die is rolled eight times, to form an eight-digit number. What is the probability that the resulting number is a multiple of 8?
  4. counting and probability

    A fair, six-sided die is rolled eight times, to form an eight-digit number. What is the probability that the resulting number is a multiple of 8?
  5. probability - confused

    A fair, six-sided die is rolled eight times, to form an eight-digit number. What is the probability that the resulting number is a multiple of 8?
  6. probability please help!!

    A fair, six-sided die is rolled eight times, to form an eight-digit number. What is the probability that the resulting number is a multiple of 8?
  7. maths

    Suppose that 10 dice are rolled. Each die is a regular 6 -sided die with numbers 1 through 6 labelled on the sides. How many different sums of all 10 numbers are possible?
  8. probability

    Two six-sided dice each have the numbers 1 through 6 on their faces. Neither die is fair, but they are both weighted the same. The probability of rolling a certain number on one die is given in the table below: # 1 2 3 4 5 6 probability …
  9. math

    Hi! I'm Maddie. I need some help on my homework. Here are three problems I need help with: A bowl contains only red marbles, blue marbles and green marbles. The probability of selecting a red marble from the bowl is 3/13. The probability …
  10. Maths

    An 8-sided die shows the numbers 1 to 8. A 6-sided die shows the numbers 1 to 6. If both dice are rolled at the same time, how many possible outcomes are there?

More Similar Questions