see in the explanation !

Step-by-step explanation:

QUESTION 1:

Facts:

"MATHEMATICS" has 11 letters.

The vowels are A, E, I, O, U, and sometimes Y.

Method: Find how many vowels are in "mathematics"

the vowels found in this word are a, e, and i. Hence, there are 3 vowels, and the probability of ANY vowel getting picked is 3/11.

QUESTION 2:

Facts:

24 pupils have 2+ books.

Method: Find the total number of students

probability: preferred outcomes/total number of outcomes

In this case, the "preferred outcomes" are the number of students with 2 or more books, and the "total outcome" is the total number of students. We are basically trying to find the number of students with 2+ books out of the total number of students there are.

"preferred outcomes": 24

"total outcomes": 42

Add up the numbers of students given in the chart to find the total. Just add the numbers in the right column, beacuse we are trying to find the # of students , so the 1st column is irrelevant .

24+14+4= 42

24/42= 4/7

Answer =D

QUESTION 3

Now the total number of students is 1,000. You may be thinking about the "total number of students" above , that is clearly different from this. BUT, here we are just using the probability we found in question 2 (4/7) to find the probability in this scenario .

Method 1: Proportion

4 x

__ = _____

7 1000

7x= 4000

x= about 571.4---> 571

Method 2: Percentage

4/7= 0.571428571---> about 57%

so if 57% of students have 2+ books, and 57% of 1,000 is 570, about 570 students have books. And since 570 is close to 571, technically speaking, both methods lead us to option A although the proportion method was more precise.

QUESTION 4:

The probability of students having no book, according to the table, is 2/21 because 4/42=2/21. Now, the total numbber of students is 1000, so we will solve a proportion again.

2 x

__= ___

21 1000

21x= 2000

x= about 95

Answer= B

QUESTION 5:

Facts:

coin is tossed 80 times.

heads: 46 times

tails: 34 times

probability of tails: 34/80 = 17/40

A

Hope this helps :)) Also brainliest would be appreciated, I stayed up pretty late working on this lol :)