Question

PLEASE I NEED THIS!! (20 points)

A six-sided fair die is rolled two times. Arrange the events in order from the event with the highest probability to the event with the lowest probability.
the probability of
getting the same
number on
each roll
the probability of
obtaining an odd
prime number
(excluding 1) on
each roll
the probability
that the difference
of the two
numbers is at
most 1
the probability
that the second
number is a
multiple of the
first number
, , ,

Answer 1

To arrange the events from highest to lowest probability: the event of the difference between two die rolls being at most 1 has the highest probability, then the second number being a multiple of the first, followed by rolling the same number twice, and finally rolling an odd prime number on each die, which has the lowest probability.

Step-by-step explanation:

To answer the question, we need to arrange the events from the highest probability to the lowest probability when a six-sided die is rolled two times:

1. 1. the probability that the difference of the two numbers is at most 1,
   2. the probability of obtaining an odd prime number (excluding 1) on each roll,
   3. the probability of getting the same number on each roll,
   4. the probability that the second number is a multiple of the first number.

Let's calculate each probability step by step.

Probability of getting the same number on each roll: There are 6 possible outcomes where both dice show the same number (1-1, 2-2, 3-3, 4-4, 5-5, 6-6) out of 36 total outcomes, so the probability is 6/36 or 1/6.

Probability of obtaining an odd prime number on each roll: The odd prime numbers on a die are 3 and 5. There are 2 possible outcomes for the first die and 2 for the second, giving us 4 total combinations (3-3, 3-5, 5-3, 5-5) out of 36, so the probability is 4/36 or 1/9.

Probability that the second number is a multiple of the first number: Considering the numbers 1 through 6, the second die will be a multiple of the first die if the first die is 1 or if both dice show 2, 3, or 6 (since 4 and 5 do not have multiples within 1-6). This gives us 1*6 + 3*1 = 9 favorable outcomes out of 36, or a probability of 9/36 which reduces to 1/4.

Probability that the difference of the two numbers is at most 1: This event includes combinations where the second number is either the same, one less, or one more than the first number. Counting these for each number on the first die gives us 17 outcomes out of 36, so the probability is 17/36.

In conclusion, the event with the highest probability is 'the difference of the two numbers is at most 1', followed by 'the second number is a multiple of the first number', then 'getting the same number on each roll', and finally 'obtaining an odd prime number on each roll' with the lowest probability.