Question

task 4: find the probability of the event below. give your answer as a fraction, then convert it to a percentage. 1. a bag of crayons contains 8 red, 14 purple, 6 yellow, and 4 green. a crayon is selected, put back, and then another crayon is selected. find each probability below. a) p(purple then yellow) b) p(green then red) c) p(two purples) d) p(two yellows)

Explanation:

Step1: Calculate total crayons

Total = $8 + 14 + 6 + 4 = 32$

Step2: Solve part (a)

First purple: $\frac{14}{32}$, then yellow: $\frac{6}{32}$. Multiply:
$\frac{14}{32} \times \frac{6}{32} = \frac{84}{1024} = \frac{21}{256}$
Percentage: $\frac{21}{256} \times 100 \approx 8.20\%$

Step3: Solve part (b)

First green: $\frac{4}{32}$, then red: $\frac{8}{32}$. Multiply:
$\frac{4}{32} \times \frac{8}{32} = \frac{32}{1024} = \frac{1}{32}$
Percentage: $\frac{1}{32} \times 100 = 3.125\%$

Step4: Solve part (c)

First purple: $\frac{14}{32}$, second purple: $\frac{14}{32}$. Multiply:
$\frac{14}{32} \times \frac{14}{32} = \frac{196}{1024} = \frac{49}{256}$
Percentage: $\frac{49}{256} \times 100 \approx 19.14\%$

Step5: Solve part (d)

First yellow: $\frac{6}{32}$, second yellow: $\frac{6}{32}$. Multiply:
$\frac{6}{32} \times \frac{6}{32} = \frac{36}{1024} = \frac{9}{256}$
Percentage: $\frac{9}{256} \times 100 \approx 3.52\%$

Answer:

a) Fraction: $\frac{21}{256}$, Percentage: $\approx 8.20\%$
b) Fraction: $\frac{1}{32}$, Percentage: $3.125\%$
c) Fraction: $\frac{49}{256}$, Percentage: $\approx 19.14\%$
d) Fraction: $\frac{9}{256}$, Percentage: $\approx 3.52\%$