Question

You might need: Calculator Problem Suppose that Antonia rolls a pair of fair six-sided dice. Let AAA be the event that the first die lands on 555 and BBB be the event that the sum of the two dice is 666. Using the sample space of possible outcomes below, answer each of the following questions. What is P(A)P(A)P, (, A, ), the probability that the first die lands on 555

Answer 1

The probability P(A), where event A is the first die landing on a 5 when rolling a pair of dice, is 1/6.

Step-by-step explanation:

Calculating the probability of the first die landing on 5 in a dice roll

Here's how to calculate the probability that the first die lands on 5:

Identify the relevant event: Event A represents the first die landing on 5.

Count the favorable outcomes: Out of the 36 possible outcomes listed in the sample space (assuming it's not provided here), only 6 of them have the first die showing 5. These are:

(5, 1), (5, 2), (5, 3), (5, 4), (5, 5), (5, 6)

Calculate the probability: Divide the number of favorable outcomes by the total number of possible outcomes:

P(A) = Number of favorable outcomes / Total number of outcomes

P(A) = 6 / 36 = 1 / 6

Therefore, the probability that the first die lands on 5 is 1/6.

Answer 2

P(A)=1/6

Step-by-step explanation:

The sample space of the two dice is given below:

[1, 1], [1, 2], [1, 3], [1, 4], [1, 5], [1, 6]

[2, 1], [2, 2], [2, 3], [2, 4], [2, 5], [2, 6]

[3, 1], [3, 2], [3, 3], [3, 4], [3, 5], [3, 6]

[4, 1], [4, 2], [4, 3], [4, 4], [4, 5], [4, 6]

[5, 1], [5, 2], [5, 3], [5, 4], [5, 5], [5, 6]

[6, 1], [6, 2], [6, 3], [6, 4], [6, 5], [6, 6]

n(S)=36

Let A be the event that the first die lands on 5

Sample Space of Event A is:

[5, 1], [5, 2], [5, 3], [5, 4], [5, 5], [5, 6]

n(A)=6

Therefore:

P(A)=n(A)/n(S)

=6/36

=1/6