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If you spin the spinner twice, what is the probability of spinning pink then brown

$4$ . If you spin the spinner twice, what is the probability of spinning pink then brown

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Probability of independent and dependent events

Full solution

Q.

4

. If you spin the spinner twice, what is the probability of spinning pink then brown

Total Colors and Frequencies: First, we need to know the total number of colors on the spinner and how many times pink and brown appear. Let's say there are $8$ sections on the spinner with $2$ pink and $2$ brown sections.
Calculate Pink Probability: Now, calculate the probability of spinning pink first. $\newline$ Probability of pink = Number of pink sections / Total number of sections = $\frac{2}{8} = \frac{1}{4}$ .
Calculate Brown Probability: Next, calculate the probability of spinning brown second. Since we're not replacing the first spin, the total number of sections is now $7$ . Probability of brown $= \frac{\text{Number of brown sections}}{\text{Total number of sections}} = \frac{2}{7}$ .
Overall Probability Calculation: Finally, multiply the probabilities of the two independent events to get the overall probability. $\newline$ Probability of pink then brown = Probability of pink $*$ Probability of brown = $\frac{1}{4}$ $*$ $\frac{2}{7}$ = $\frac{2}{28}$ = $\frac{1}{14}$ .

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