Lim Vx+a - 3x-a<br>Evaluate<br>X->a<br>-<br>x-a

A standard pair of six-sided dice is rolled. What is the probability of rolling a sum less than 7? Express your answer as a frac

zzz [600]

Answer:

0.4167 is the probability of rolling a sum less than 7.

Step-by-step explanation:

We are given the following in the question:

Event: A standard pair of six-sided dice is rolled

A: rolling a sum less than 7

Sample space:

{(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)}

A:

{(1,1),(1,2),(1,3),(1,4),(1,5),(2,1),(2,2),(2,3),(2,4),(3,1),(3,2),(3,3),(4,1),(4,2),(5,1)}

Formula:

$\text{Probability} = \displaystyle\frac{\text{Number of favourable outcomes}}{\text{Total number of outcomes}}$

$P(A) = \dfrac{15}{36} = 0.4167$

0.4167 is the probability of rolling a sum less than 7.

8 0

3 years ago

Use the diagram and the following equation to solve for x.

Lemur [1.5K]

Starting with 113+ (2x+5)=180, combine like terms and to get 118+2x=180. Subtract 180-118, which gives you 62. Then you have 2x=62. Divide both sides by 2 to get a final answer of x=31.

8 0

3 years ago

Read 2 more answers

There is a boardwalk game at Point Pleasant where you are blindfolded to throw darts at a board full of balloons. Each time a da

arlik [135]

The given number of balloons, green = 10, purple = 4, red = 5, tie-dye = 2, black = 3, gives;

a. 5/138

b. 25/276

c. 5/1012

d. 35/46

<h3>How can the different probabilities be calculated mathematically?</h3>

Given parameters;

Number of balls;

Green = 10

Purple = 4

Red = 5

Tie-dye = 2

Black = 3

Mode of selection = Without replacement

Number of balloons = 10+4+5+2+3 = 24

a. Probability of popping a red balloon = 5/24

Probability of popping a second red balloon = 4/23

Therefore;

Probability of popping two reds consecutively = 5/24 × 4/23 = 5/138

b. Probability of popping a red balloon = 5/24

Probability of popping a green balloon next = 10/23

Therefore;

Probability of popping a red and then a green balloon = 5/24 × 10/23 = 25/276

c. Probability that the first balloon that pops is a red = 5/24

Next balloon is a black = 3/23

Third balloon is red = 4/22

The probability, <em>P</em>, is therefore;

P = 5/24 × 3/23 × 4/22 = 5/1012

d. The probability that the first balloon is a tie-dye = 2/24 = 1/12

Therefore;

Probability that the first balloon is not a tie-dye = 1 - 1/12 = 11/12

Probability that the second balloon is not a tie-dye = 21/23

Similarly;

Probability that the third balloon is not a tie-dye = 20/22 = 10/11

Which gives;

The probability, <em>P</em>, of popping anything but a tie-dye on three consecutive throws is therefore;

P = 11/12 × 21/23 × 10/11 = 35/46

Learn more about probability theory in mathematics?

brainly.com/question/13604758

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7 0

1 year ago

Meg has 26 toy ponies.She gets 6 more for her birthday.She displays half of them on a shelf and puts the rest in a box.How many

Mazyrski [523]

Answer:

16 ponies are displayed

Step-by-step explanation:

First you need to add 26 and 6 to get 32.Then you need to cut 32 in half or divide it by 2 for your answer.

5 0

3 years ago

Read 2 more answers

Evaluate 805 divide by 5

Ket [755]

805 divided by 5 equals 161

4 0

3 years ago

Read 2 more answers

Lim Vx+a - 3x-aEvaluateX->a-x-a​

Lim Vx+a - 3x-aEvaluateX->a-x-a