All questions of Data Handling for Class 8 Exam

To find the probability that the number on the card is divisible by 5, we need to determine the number of favorable outcomes (cards divisible by 5) and the total number of possible outcomes (all cards in the box).

Total number of possible outcomes:
The box contains 19 cards with numbers 1, 2, 3, ..., 19. Therefore, the total number of possible outcomes is 19.

Number of favorable outcomes:
Out of the 19 cards, we need to identify the ones that are divisible by 5. The numbers divisible by 5 in the given range are 5, 10, 15, and 20. However, since there is no card with the number 20, we can exclude it. Therefore, there are 3 favorable outcomes (cards with numbers 5, 10, and 15).

Probability calculation:
Probability is the ratio of favorable outcomes to total outcomes.

Probability = Number of favorable outcomes / Total number of possible outcomes
= 3 / 19

Therefore, the probability that the number on the card is divisible by 5 is 3/19.

Answer: Option A) 3/19

Solution:

When two dice are thrown, the possible outcomes are:

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

There are 36 possible outcomes when two dice are thrown.

Finding the probability of getting an even number as the sum:

When two dice are thrown, the sum of the numbers on them can range from 2 to 12.

The possible sums that are even are 2, 4, 6, 8, 10, and 12.

Out of the 36 possible outcomes, there are 18 outcomes where the sum is even:

2 (1, 1)
4 (1, 3), (3, 1), (2, 2)
6 (1, 5), (5, 1), (2, 4), (4, 2), (3, 3)
8 (2, 6), (6, 2), (4, 4)
10 (4, 6), (6, 4), (5, 5)
12 (6, 6)

Therefore, the probability of getting an even number as the sum is 18/36 or 1/2.

Hence, option A is the correct answer.

Total number of possible outcomes when three coins are tossed together:

To find the total number of possible outcomes when three coins are tossed together, we can use the concept of multiplication principle.

The Multiplication Principle:
The multiplication principle states that if there are m ways to do one thing and n ways to do another, then there are m * n ways to do both things.

Analysis:
When a coin is tossed, there are two possible outcomes - either it can land heads up or tails up. So, for one coin, there are 2 possible outcomes.

Applying the multiplication principle:
Since we have three coins, we can apply the multiplication principle to find the total number of possible outcomes.

For the first coin, there are 2 possible outcomes (heads or tails).
For the second coin, there are also 2 possible outcomes (heads or tails).
For the third coin, there are again 2 possible outcomes (heads or tails).

Using the multiplication principle, the total number of possible outcomes when three coins are tossed together is:

2 * 2 * 2 = 8

Answer:
Therefore, the correct answer is option A) 8.

Given Information:
- The mean of five numbers is 27.
- If one of the numbers is excluded, the mean becomes 25.

Solution:

Step 1: Find the sum of the five numbers
Let the five numbers be a, b, c, d, and e.
According to the given information, the mean of the five numbers is 27. Therefore, the sum of the five numbers = 27 * 5 = 135

Step 2: Find the sum of the four numbers when one number is excluded
When one number is excluded, the mean of the remaining four numbers is 25. Therefore, the sum of the four numbers = 25 * 4 = 100

Step 3: Determine the excluded number
Subtract the sum of the four numbers from the sum of the five numbers to find the excluded number:
135 - 100 = 35
Therefore, the excluded number is 35.
Therefore, the correct answer is option D) 35.

Mean of the average time spent in a week by the 5 people doing social work can be found by using the formula:

Mean = (Sum of all observations) / (Total number of observations)

Here, the sum of all observations is:

10 + 7 + 13 + 20 + 15 = 65

And the total number of observations is 5.

So, the mean is:

Mean = 65 / 5 = 13 hrs

Therefore, the correct option is D, which is 13 hrs.

Probability of getting a multiple of 3 when throwing a dice:
To calculate the probability of getting a multiple of 3 when throwing a dice, we first need to determine the total number of possible outcomes and then find the number of favorable outcomes.

Total number of possible outcomes:
When a dice is thrown once, there are 6 possible outcomes as a standard dice has 6 faces numbered from 1 to 6.

Favorable outcomes:
Multiples of 3 on a dice are 3 and 6. So, there are 2 favorable outcomes.

Calculating the probability:
Probability = Number of favorable outcomes / Total number of possible outcomes
Probability = 2 / 6
Probability = 1/3
Therefore, the probability of getting a multiple of 3 when throwing a dice is 1/3.

Solution:

Face cards are the cards with picture on it, i.e., Jack, Queen, and King.

There are 2 red suits in a deck of cards - Hearts and Diamonds. Each suit has 3 face cards. Hence, there are a total of 6 red face cards in a deck.

Total number of cards in a deck = 52

Probability of drawing a red face card = (number of red face cards) / (total number of cards)

= 6 / 52

= 3 / 26

Therefore, the probability of drawing a red face card is 3/26.

Option A is the correct answer.