Pooja R.

To determine if the points (5, 4) and (4, 5) represent the same point, we can compare their coordinates.

The point (5, 4) has coordinates (x, y) = (5, 4), while the point (4, 5) has coordinates (x, y) = (4, 5).

Since the order of the coordinates matters, these points are different. The first point is located at (5, 4), and the second point is located at (4, 5). Therefore, they do not represent the same point in a Cartesian coordinate system.

To find the probability of drawing a red ball from the bag, we need to determine the ratio of the number of red balls to the total number of balls.

Number of red balls = 2

Total number of balls = 3 (blue) + 2 (red) = 5

The probability (PP) is given by the formula:

P(Event)=Number of Favorable OutcomesTotal Number of Possible OutcomesP(Event)=Total Number of Possible OutcomesNumber of Favorable Outcomes

P(Red Ball)=25P(Red Ball)=52

Therefore, the probability of drawing a red ball from the bag is 2552.

To find the probability of selecting a prime number from the numbers 1 through 20, we need to determine the count of prime numbers in that range and divide it by the total count of numbers.

Prime numbers between 1 and 20 are: 2, 3, 5, 7, 11, 13, 17, 19.

Number of favorable outcomes (prime numbers) = 8

Total number of possible outcomes (numbers from 1 to 20) = 20

The probability (PP) is given by the formula:

P(Event)=Number of Favorable OutcomesTotal Number of Possible OutcomesP(Event)=Total Number of Possible OutcomesNumber of Favorable Outcomes

P(Prime Number)=820=25P(Prime Number)=208=52

Therefore, the probability of selecting a prime number from the numbers 1 through 20 is 2552.

A standard six-sided die has the numbers 1 through 6. To find the probability of getting an even number when throwing the die, you need to determine how many outcomes satisfy the condition and divide it by the total number of possible outcomes.

(i) Probability of Getting an Even Number:

• Even numbers on a die are 2, 4, and 6.

Number of favorable outcomes = 3 (2, 4, 6)

Total number of possible outcomes = 6 (1, 2, 3, 4, 5, 6)

The probability (PP) is given by the formula:

P(Event)=Number of Favorable OutcomesTotal Number of Possible OutcomesP(Event)=Total Number of Possible OutcomesNumber of Favorable Outcomes

P(Even Number)=36=12P(Even Number)=63=21

Therefore, the probability of getting an even number when throwing a die is 1221.

A histogram is used to represent the distribution of continuous data, typically grouped into intervals or bins. Let's analyze the given scenarios:

(i) The number of letters for different areas in a postman’s bag:

• This scenario involves discrete data, as the number of letters cannot be measured in continuous intervals. A bar graph or a simple bar chart may be more appropriate for displaying this type of data, where each bar represents the count of letters for a specific area.

(ii) The height of competitors in an athletics meet:

• This scenario involves continuous data, as height can vary within a range and is measured on a continuous scale. A histogram would be suitable for representing the distribution of heights, as it allows for the visualization of the frequency distribution across different height intervals.

Therefore, for the height of competitors in an athletics meet, a histogram would be more appropriate to show the distribution of heights.