Question

hat did the girl rock say to the bod the answer to any question below in the code key. notice the letter nexts letter in the box at the bottom of the page that contains the problem numep working and you will discover the answer to the title question.1 if a coin is tossed, what is the probability of getting a head?2 if a coin is tossed, what is the probability of getting a tail?3 suppose a coin is tossed 100 times. about how many times would you expect to get heads?suppose you roll a regular 6-faced die. what is the probability of rolling:4 a 6?5 a 2?6 a 4?7 suppose you roll a 6-faced die 90 times. about how many times would you expect to get a 5?suppose a jar contains 5 red marbles, 4 white marbles, and 3 blue marbles. if a marble is drawn at random from the jar, what is the probability that it is:8 red?9 white?10 blue?a spinner is pictured at the right. if the arrow is spun, what is the probability that the spinner lands on:11 2?12 3?13 5?14 an even number?15 a number less than 3?16 suppose the arrow is spun 50 times. about how many times expect the spinner to land on an odd number?

Explanation:

Step1: Define coin probability formula

Probability = $\frac{\text{Favorable Outcomes}}{\text{Total Outcomes}}$
For a coin, total outcomes = 2 (head, tail)

Step2: Solve Q1 (head probability)

Favorable outcomes = 1 (head)
$\text{Probability} = \frac{1}{2}$

Step3: Solve Q2 (tail probability)

Favorable outcomes = 1 (tail)
$\text{Probability} = \frac{1}{2}$

Step4: Solve Q3 (expected heads)

Expected value = Probability × Trials
$\text{Expected heads} = \frac{1}{2} \times 100 = 50$

Step5: Define die probability formula

Total outcomes for 6-faced die = 6

Step6: Solve Q4 (roll a 6)

Favorable outcomes = 1
$\text{Probability} = \frac{1}{6}$

Step7: Solve Q5 (roll a 2)

Favorable outcomes = 1
$\text{Probability} = \frac{1}{6}$

Step8: Solve Q6 (roll a 4)

Favorable outcomes = 1
$\text{Probability} = \frac{1}{6}$

Step9: Solve Q7 (expected 5s)

Expected value = $\frac{1}{6} \times 90 = 15$

Step10: Calculate total marbles

Total marbles = $5 + 4 + 3 = 12$

Step11: Solve Q8 (red marble)

Favorable outcomes = 5
$\text{Probability} = \frac{5}{12}$

Step12: Solve Q9 (white marble)

Favorable outcomes = 4
$\text{Probability} = \frac{4}{12} = \frac{1}{3}$

Step13: Solve Q10 (blue marble)

Favorable outcomes = 3
$\text{Probability} = \frac{3}{12} = \frac{1}{4}$

Step14: Define spinner total sections

Spinner has 5 equal sections

Step15: Solve Q11 (land on 2)

Favorable outcomes = 1
$\text{Probability} = \frac{1}{5}$

Step16: Solve Q12 (land on 3)

Favorable outcomes = 1
$\text{Probability} = \frac{1}{5}$

Step17: Solve Q13 (land on 5)

Favorable outcomes = 1
$\text{Probability} = \frac{1}{5}$

Step18: Solve Q14 (even number)

Even numbers: 2,4 (2 outcomes)
$\text{Probability} = \frac{2}{5}$

Step19: Solve Q15 (number <3)

Numbers <3: 1,2 (2 outcomes)
$\text{Probability} = \frac{2}{5}$

Step20: Solve Q16 (expected odd numbers)

Odd numbers:1,3,5 (3 outcomes), probability = $\frac{3}{5}$
Expected value = $\frac{3}{5} \times 50 = 30$

Answer:

1. $\frac{1}{2}$
2. $\frac{1}{2}$
3. $50$
4. $\frac{1}{6}$
5. $\frac{1}{6}$
6. $\frac{1}{6}$
7. $15$
8. $\frac{5}{12}$
9. $\frac{1}{3}$
10. $\frac{1}{4}$
11. $\frac{1}{5}$
12. $\frac{1}{5}$
13. $\frac{1}{5}$
14. $\frac{2}{5}$
15. $\frac{2}{5}$
16. $30$