Question

2 - 11. nicole has a machine that will produce a number from 1 through 50 when she pushes a button. explore by highlighting numbers on the 2 - 11 hw etool (cpm). if she pushes the button, what is: a. p(multiple of 10)? b. p(not 100)? c. p(not a multiple of 4)? d. p(one - digit number)

Explanation:

Step1: Determine total number of outcomes

The machine produces numbers from 1 through 50, so the total number of possible outcomes is $n = 50$.

Step2: Calculate probability for part a

The multiples of 10 from 1 - 50 are 10, 20, 30, 40, 50. So the number of favorable outcomes $m_1=5$. The probability $P(\text{multiple of 10})=\frac{m_1}{n}=\frac{5}{50}=\frac{1}{10}$.

Step3: Calculate probability for part b

The number 100 is not in the range 1 - 50. So the number of times 100 can occur is 0. Then $P(\text{not }100)=\frac{50 - 0}{50}=1$.

Step4: Calculate probability for part c

The multiples of 4 from 1 - 50 are $4,8,\cdots,48$. We use the arithmetic - sequence formula $a_n=a_1+(n - 1)d$, where $a_1 = 4$, $d = 4$, and $a_n=48$. Solving $48=4+(n - 1)\times4$ gives $n = 12$. So the number of favorable outcomes $m_3 = 12$. Then $P(\text{not a multiple of 4})=1 - P(\text{multiple of 4})=1-\frac{12}{50}=\frac{38}{50}=\frac{19}{25}$.

Step5: Calculate probability for part d

The one - digit numbers from 1 - 50 are 1, 2, 3, 4, 5, 6, 7, 8, 9. So the number of favorable outcomes $m_4 = 9$. Then $P(\text{one - digit number})=\frac{9}{50}$.

Answer:

a. $\frac{1}{10}$
b. 1
c. $\frac{19}{25}$
d. $\frac{9}{50}$