Explanation

A die has 6 faces with dots numbered from 1 to 6.

Event: The dots on the top are greater than 2 → possible outcomes: 3, 4, 5, 6

Number of favorable outcomes = 4

Total possible outcomes = 6

Probability = Favorable outcomes / Total outcomes = 4/6 = 2/3

Explanation

The probability that someone is between Aviva and Naomi

• Aviva is the 37th person.

• Naomi is the 67th person.

• "Between" refers to people aged 37 to 67, i.e., positions 38 through 66.

Number of people between them = 66 − 38 + 1 = 29 people

There are 100 people total.

So the probability that a randomly chosen person is between them is:

$$\frac{\mathrm{<font\; color="\#0000ff"><span\; style="background-color:\; rgb(255,\; 255,\; 0);">29</span></font>}}{\mathrm{<span\; style="font-size:\; 0.875rem;"><font\; color="\#0000ff"\; style="background-color:\; rgb(255,\; 255,\; 0);">100</font><span\; style="font-family:\; Overpass,\; sans-serif;"></span></span>}}$$

Explanation

 Let's analyze the problem:

• Total marbles in the jar: 5 (red, white, blue, yellow, and 1 more color)

• 4 marbles are removed.

• Find the probability that the yellow marble was removed.

Step 1: Total ways to remove 4 marbles from 5

Step 2: Number of ways to remove 4 marbles, including yellow

To include the yellow marble, we must select the yellow marble and 3 others from the remaining 4 marbles:

Step 3: Probability yellow marble is removed

Explanation

 We are given:

• Red balls = 8

• Blue balls = 7

• Green balls = 6

Total balls = 8 + 7 + 6 = 21

We are asked to find the probability that the ball is neither red nor green.

That means we want the probability that the ball is blue.

Number of favorable outcomes = Number of blue balls = 7

Probability = (Favorable outcomes) / (Total outcomes)

= 7/31

=1/3
$$721=13frac{7}{21} = frac{1}{3}

Explanation

Let number of coins = 3x, 5x, 4x
→ Total value = 264
→ $3x+10x+20x=33x=264\Rightarrow x=8$

$\mathrm{<br>}$2 coins = 5x = 5 × 8 = 40 coins
→ Value = 40 × 2 = 80 

So to get 66, x = 6

33x = 264 → x = 8
33x = 198 → x = 6 → 3x = 18 coins → 1 coins = 18

So likely in your example:

• Ratio = 3:5:4

• Total = 198

• x = 6

• 2 coins = 5x = 30 coins

• Value = ₹60

So if 2 coins value = 66, x = 6.6, which is not clea

Explanation

If a constant is added to each value, the mean increases by that constant.

New mean = 6 + 3 = 9.

Explanation

Mean = (9 + 8 + 10 + x + 12) / 5 = 15

39 + x = 75 → x = 75 - 39 = 36

Explanation

Simple Interest = Principal × Rate × Time

$$= 300 times tfrac{5}{100} times 1 = mathbf{15}.$$

Explanation

A pie graph (or pie chart) is divided into sectors, where each sector represents a part of the whole.

The size of each sector corresponds to the proportion of the category it represents.

Explanation

To find the weighted mean:

Step 1: Calculate the weighted sum

Weighted sum = (18_2) + (19_3) + (20_4) + (21_2) + (22_1) + (23_1) + (24*1)

= 36 + 57 + 80 + 42 + 22 + 23 + 24

= 284

Step 2: Calculate the total weight

Total weight = 2 + 3 + 4 + 2 + 1 + 1 + 1

= 14

Step 3: Calculate the weighted mean

Weighted mean = Weighted sum / Total weight

= 284 / 14

= 20.286