Grade 10  Probability
(Sample Printed worksheet)
Answer The Following  
1)  Two dice are rolled. What is the probability that the two numbers add up to a prime number? 
2)  A bag contains 3 red balls, 5 blue balls, and 7 green balls. Carol draws 2 balls out of the bag. What is the probability that she gets a red ball and a blue ball? 
3)  Coin A is flipped 3 times and coin B is flipped 4 times. What is the probability that the number of heads obtained from flipping the two coins is the same? 
4)  A tyre manufacturer keeps the record of how much distance the tyres manufactured by the company travel before failing. They find the following data
If Sandra buys a tyre from them, what is the probability that it will last more than 20000 kilometers? 
5)  What is the probability that a leap year will contain 53 Tuesdays? 
Choose correct answer(s) from given choice  
6)  A poll is taken among people working in Atlanta. The aim was to see what their annual salaries were.
If you choose a person at random from this group, what is the probability that he or she earns more than 75000 annually?

7)  Nancy selects 3 numbers randomly from the following set of 5 numbers 5, 3, 1, 6 and 9. He puts them in the form of a proper fraction of the type
What is the probability that you will get a fraction greater than

8)  Michelle is participating in a race. The probability that she will come first in the race is 0.3. The probability that she will come second in the race is 0.2. The probability that she will come in 3rd is 0.4, and the probability that she will be 4th is 0.1. What is the probability that she will win 2nd position or better in the race?

9)  There are 4 pens belonging to 4 students. The pens were put into a box, and each student pulls out an pen one after the other. What is the probability that each student gets his or her own pen?

10)  If a prime number is less than 23, what is the probability that it is also less than 17.

Answers
1)15 
36 
Step 1  
The two dice that are rolled can show any of these values Dice 1 : 1, 2, 3, 4, 5, 6 Dice 2 : 1, 2, 3, 4, 5, 6 So we can get a total of 36 combinations between them (6 x 6)  
Step 2  
If we take one value from the list of possible values from each Dice, we get numbers ranging from 2 (when both Dice show 1) to 12 (when both dice show 6). Let's enumerate the prime numbers between 2 and 12. They are 2, 3, 5, 7 and 11 We need to see in how many ways we can get each of these values Let's put the value rolled by the dice as (x,y), where x is the value rolled by Dice 1, and y the value rolled by Dice 2  2: The only way to get this is when we roll (1,1). 1 possibility  3: We can get this by (1,2) or (2,1). 2 possibilities.  5: We can get this by (2,3), (3,2), (1,4) or (4,1). 4 possibilities.  7: We can get this by (1,6), (2,5), (3,4), (4,3), (5,2), (6,1). 6 possibilities.  11: We can get this by (5,6), or (6,5). 2 Possibilities This gives us a total of 1 + 2 + 4 + 6 + 2 = 15 possible ways to get a prime number  
Step 3  
So the probability of getting the two numbers add up to a prime is

2)
15 
105 
Step 1  
There are a total of 3+5+7 = 15 balls in the bag  
Step 2  
The number of ways to pick out 2 balls from a set of 15 balls is 15 C2 = 15 x (151)/2 = 105  
Step 3  
The number of ways to pick a red ball and a blue ball is obtained by multiplying the number of the balls of each of these colors. This is 3 x 5 = 15  
Step 4  
The probability that she gets a red ball and a blue ball is therefore

3)
35 
128 
4)
1260 
2000 
Step 1  
First we need to find the total number of tyres that are given here  
Step 2  
We add the number of tyres 80 + 300 + 360 + 504 + 756 = 2000  
Step 3  
To find the probability that the tyre Sandra purchased would last more than 20000 kilometers, we need to add the number of tyres that lasted more than 20000 kilometers This is 504 + 756 = 1260  
Step 4  
The probability that the tyre lasts more than 20000 km =

5)
2 
7 
Step 1  
There are 366 days in a leap year  
Step 2  
If we divide 366 by 7 (since there are seven days in a week), we will get an answer of 52, with a remainder of 2 This means that a leap year will have 52 Sundays, 52 Mondays, 52 Tuesdays, 52 Wednesdays, 52 Thursdays, 52 Fridays and 52 Saturdays. Apart from these there will be two other days. This means that there will be two weekdays that occur 53 times.  
Step 3  
The two days could be (Sunday, Monday), (Monday, Tuesday), (Tuesday, Wednesday), (Wednesday, Thursday), (Thursday, Friday), (Friday, Saturday), or (Saturday, Sunday)  a total of seven combinations  
Step 4  
Out of these seven combinations, two of them have a Tuesday  
Step 5  
So the probability of either of those two days being a Tuesday is

6) b.
8820 
10000 
Step 1  
First we need to find the total number of people among whom the poll was taken  
Step 2  
We add the number of people in the various sets 360 + 820 + 1940 + 2752 + 4128 = 10000  
Step 3  
To find the probability that the the random person chosen has a salary of more than 75000 , we need to add the number of people who have salaries greater than this number This is 1940 + 2752 + 4128 = 8820  
Step 4  
So 8820 people out of a total of 10000 earn an annual salary greater than 75000 The probability that the randomly chosen person has a salary greater than 75000 =

7) a.
12 
30 
Step 1  
We need to select 3 numbers out of the 5 given in order to get a fraction of the form
We are also told it is a proper fraction, so b should be greater than c  
Step 2  
Let's put the integers in a sorted manner. We get 1, 3, 5, 6 and 9  
Step 3  
Now we need to see how many proper fractions can be formed from them A proper fraction of the type
Let's assume we use one of the integers in the list above as the whole number a We now can select b and c from the remaining 4 integers We can select 2 integers from 4 in 4C2 =
For any pair we select, one will be greater than the other, and the smaller integer will form the numerator and the larger one the denominator  Note: that the other way won't work  if the numerator is larger than the denominator it is not a proper fraction So for each of the 5 integers, if we select one as the whole number, we get 6 possible combinations of numerator and denominator that can form a proper fraction This means there are 5x6 = 30 possible proper fractions of the form
 
Step 4  
Now we need to figure out how many of these 30 fractions are greater than
In gt, we see that the whole number is 5, the numerator is 17 and the denominator is 18 We see that the numerator 17 is larger than the largest number in the set of numbers given to us, and the denominator 18 is one larger than 17 The implication of this is that
So we only need to count the fractions that have the whole number greater than 5 These are the fractions that will have the whole numbers as 6 and 9  
Step 5  
Now, remember there are 30 proper fractions you can form from this list of number From our analysis above, we also saw that for each number selected as the whole number, we can form 6 fractions from this list of numbers  
Step 6  
So using each of the numbers from 6 and 9 as the whole number, we can form 6 proper fractions The total number of fractions that can be formed using 6 and 9 as the whole number = 6 x 2 = 12  
Step 7  
Out of the 30 fractions, 12 will be greater than
 
Step 8  
The probability is therefore =

8) a. 0.5
Step 1 
We are looking for the probability that she will come 2nd or better in the race This is the probability that she will either win the race or be 2nd Since she can be first or second, the probabilities can be added 
Step 2 
The probability that she will be first is 0.3 The probability that she will be in second place is 0.2 
Step 3 
Adding them, we get 0.3 + 0.2 = 0.5 
9) b.
1 
24 
Step 1  
We have 4 pens and 4 students. Let's first see in how many different ways can the pens be distributed among the students  
Step 2  
We know that 4 objects can be distributed in 4 ! = 4 x 3 x...x 1 = 24 ways  
Step 3  
Out of these 24 ways, there is only one distribution where each student got his or her own pen  
Step 4  
So the probability of each student getting his or her own pen =

10) c. 3/4
Step 1 
There are 8 prime numbers (2, 3, 5, 7, 11, 13, 17, 19) which are less than 23 Of these 6 are less than 17 
Step 2 
Therefore probability is 6/8 = 3/4 