The probability of an event expresses the likelihood of the event occurring. It is a ratio that compares the number of favorable outcomes to the number of possible outcomes.
B
The probability of an event expresses the likelihood of the event occurring. It is a ratio that compares the number of favorable outcomes to the number of possible outcomes.
C
The probability of an event expresses the likelihood of the event occurring. It is a ratio that compares the number of favorable outcomes to the number of possible outcomes.
D
The probability of an event expresses the likelihood of the event occurring. It is a ratio that compares the number of favorable outcomes to the number of possible outcomes.
A
1/10
B
1
C
19/25
D
9/50
Practice makes perfect
We want to determine the probability that the machine will produce a multiple of 10. Let's start by recalling that we can find the probability of an event
by calculating a ratio of the number of favorable outcomes to the number of possible outcomes.
P(event) = Number of favorable outcomes/Number of possible outcomes
Let's consider a machine that will produce a number from 1 through 50 after pushing a button. Then, the number of possible outcomes is 50 because there are 50 numbers from 1 through 50. To find the number of favorable outcomes, let's find all the numbers from 1 through 50 that are multiples of 10.
ccccc 1 & 2 & 3 & 4 & 5 [0.1em] 6 & 7 & 8 & 9 & 10 [0.1em] 11 & 12 & 13 & 14 & 15 [0.1em] 16 & 17 & 18 & 19 & 20 [0.1em] 21 & 22 & 23 & 24 & 25 [0.1em] 26 & 27 & 28 & 29 & 30 [0.1em] 31 & 32 & 33 & 34 & 35 [0.1em] 36 & 37 & 38 & 39 & 40 [0.1em] 41 & 42 & 43 & 44 & 45 [0.1em] 46 & 47 & 48 & 49 & 50
Since there are 5 multiples of 10 between 1 and 50, the number of favorable outcomes is 5. Let's calculate the probability of getting a multiple of 10 using this information.
<deduct>
P(\text{multiple of }10) = \dfrac{\text{Number of favorable outcomes}}{\text{Number of possible outcomes}}
Number of favorable outcomes= 5, Number of possible outcomes= 50
P(\text{multiple of }1
0) = \dfrac{{\color{#FF0000}{5}}}{{\color{#A800DD}{50}}}
a/b=.a /5./.b /5.
P(\text{multiple of }10) =\dfrac{5\div 5}{50\div 5}
Calculate quotient
P(\text{multiple of }10) =\dfrac{1}{10}
</deduct>
The probability of getting a multiple of 10 is 110.
Now we are asked to find the probability that the machine will produce a number that is not 100. We can do this just as we did in Part A. In this case, the number of favorable outcomes is 0 because each number from 1 through 50 is not equal to 100. Like in Part A, the number of possible outcomes is 50.
P(not100) = Number of favorable outcomes/Number of possible outcomes
The probability of getting a number not equal to 100 is 1.
We want to find the probability that the machine will produce a number that is not a multiple of 4. Let's do this the same way we did in Part A. Again, the number of possible outcomes is 50. To find the number of favorable outcomes, let's find all the numbers from 1 through 50 that are not multiples of 4.
ccccc 1 & 2 & 3 & 4 & 5 [0.1em] 6 & 7 & 8 & 9 & 10 [0.1em] 11 & 12 & 13 & 14 & 15 [0.1em] 16 & 17 & 18 & 19 & 20 [0.1em] 21 & 22 & 23 & 24 & 25 [0.1em] 26 & 27 & 28 & 29 & 30 [0.1em] 31 & 32 & 33 & 34 & 35 [0.1em] 36 & 37 & 38 & 39 & 40 [0.1em] 41 & 42 & 43 & 44 & 45 [0.1em] 46 & 47 & 48 & 49 & 50
There are 38 numbers between 1 and 50 that are not a multiple of 4. This means that the number of favorable outcomes is 38. Let's calculate the probability of getting a number that is not a multiple of 4 using this information.
P(not a multiple of4) = Number of favorable outcomes/Number of possible outcomes
The probability of getting a number that is not a multiple of 4 is 1925.
We are asked to find the probability that the machine will produce a one-digit number. Again, the number of possible outcomes is 50. To find the number of favorable outcomes, let's find all the numbers from 1 through 50 that have only one digit.
ccccc 1 & 2 & 3 & 4 & 5 [0.1em] 6 & 7 & 8 & 9 & 10 [0.1em] 11 & 12 & 13 & 14 & 15 [0.1em] 16 & 17 & 18 & 19 & 20 [0.1em] 21 & 22 & 23 & 24 & 25 [0.1em] 26 & 27 & 28 & 29 & 30 [0.1em] 31 & 32 & 33 & 34 & 35 [0.1em] 36 & 37 & 38 & 39 & 40 [0.1em] 41 & 42 & 43 & 44 & 45 [0.1em] 46 & 47 & 48 & 49 & 50
There are 9 one-digit numbers between 1 and 50, which means that the number of favorable outcomes is 9. With this in mind, let's find the probability of getting a one-digit number.
P(one-digit number) = 9/50
The probability of getting a one-digit number is 950.
