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Math  /  Data & Statistics

QuestionYou spin the spinner twice.
What is the probability of landing on an even number and then landing on an 8?8 ? Write your answer as a percentage rounded to the nearest tenth. □\square \% Submit

Studdy Solution

STEP 1

1. The spinner has five equal sections numbered 5, 6, 7, 8, and 9.
2. Each section has an equal probability of being landed on.
3. The events of spinning the spinner are independent.

STEP 2

1. Determine the probability of landing on an even number on the first spin.
2. Determine the probability of landing on an 8 on the second spin.
3. Calculate the combined probability of both events occurring in sequence.
4. Convert the probability to a percentage and round to the nearest tenth.

STEP 3

Identify the even numbers on the spinner:
The even numbers are 6 and 8.

STEP 4

Calculate the probability of landing on an even number:
There are 2 even numbers out of 5 total numbers.
P(even number)=25 P(\text{even number}) = \frac{2}{5}

STEP 5

Calculate the probability of landing on an 8:
There is 1 number 8 out of 5 total numbers.
P(8)=15 P(8) = \frac{1}{5}

STEP 6

Calculate the combined probability of both events occurring in sequence:
P(even number then 8)=P(even number)×P(8)=25×15=225 P(\text{even number then 8}) = P(\text{even number}) \times P(8) = \frac{2}{5} \times \frac{1}{5} = \frac{2}{25}

STEP 7

Convert the probability to a percentage and round to the nearest tenth:
225=0.08 \frac{2}{25} = 0.08
Convert to percentage:
0.08×100=8% 0.08 \times 100 = 8\%
The probability of landing on an even number and then landing on an 8 is:
8.0% \boxed{8.0\%}

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