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QuestionFind the probabilities of these spins: red first, cyan second, blue third; blue first, blue second, red third; red on all spins.

Studdy Solution

STEP 1

Assumptions1. The spinner has six sectors. . Each sector has an equal chance of being landed on.
3. The spinner is spun three times.
4. If the spinner lands on a border, the spin does not count and another spin is made.
5. The colors of the sectors are not specified, but we assume there is at least one sector of each color red, cyan, and blue.

STEP 2

We first need to understand the concept of probability. The probability of an event is defined as the number of ways that event can occur divided by the total number of outcomes. In this case, since each sector has an equal chance of being landed on, the probability of landing on a specific color is1/6.
(Color)=16(Color) = \frac{1}{6}

STEP 3

The probability of multiple independent events occurring is the product of their individual probabilities. In this case, the spins are independent events, so the probability of spinning red on the first spin, cyan on the second spin, and blue on the third spin is the product of the probabilities of these three events.
(Red,Cyan,Blue)=(Red)×(Cyan)×(Blue)(Red, Cyan, Blue) =(Red) \times(Cyan) \times(Blue)

STEP 4

Substitute the probability of each color into the equation.
(Red,Cyan,Blue)=16×16×16(Red, Cyan, Blue) = \frac{1}{6} \times \frac{1}{6} \times \frac{1}{6}

STEP 5

Calculate the probability.
(Red,Cyan,Blue)=1216(Red, Cyan, Blue) = \frac{1}{216}

STEP 6

Similarly, we can calculate the probability of spinning blue on the first spin, blue on the second spin, and red on the third spin.
(Blue,Blue,Red)=(Blue)×(Blue)×(Red)(Blue, Blue, Red) =(Blue) \times(Blue) \times(Red)

STEP 7

Substitute the probability of each color into the equation.
(Blue,Blue,Red)=16×16×16(Blue, Blue, Red) = \frac{1}{6} \times \frac{1}{6} \times \frac{1}{6}

STEP 8

Calculate the probability.
(Blue,Blue,Red)=1216(Blue, Blue, Red) = \frac{1}{216}

STEP 9

Finally, we calculate the probability of spinning red on every spin.
(Red,Red,Red)=(Red)×(Red)×(Red)(Red, Red, Red) =(Red) \times(Red) \times(Red)

STEP 10

Substitute the probability of red into the equation.
(Red,Red,Red)=6×6×6(Red, Red, Red) = \frac{}{6} \times \frac{}{6} \times \frac{}{6}

STEP 11

Calculate the probability.
(Red,Red,Red)=216(Red, Red, Red) = \frac{}{216}So, the probability of spinning red on the first spin, cyan on the second spin, and blue on the third spin is/216. The probability of spinning blue on the first spin, blue on the second spin, and red on the third spin is also/216. The probability of spinning red on every spin is also/216.

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