Question

task 5: 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, is not put back, and then another crayon is selected. find each probability below. a) p(yellow then red) b) p(purple then green) c) p(two reds) d) p(two greens)

Explanation:

First, calculate total number of crayons:
$8 + 14 + 6 + 4 = 32$

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a) Step1: Probability of yellow first

$\text{P(yellow)} = \frac{6}{32} = \frac{3}{16}$

a) Step2: Probability of red (no replacement)

Total crayons now = 31, so $\text{P(red)} = \frac{8}{31}$

a) Step3: Multiply the two probabilities

$\text{P(yellow then red)} = \frac{3}{16} \times \frac{8}{31} = \frac{24}{496} = \frac{3}{62}$

a) Step4: Convert to percentage

$\frac{3}{62} \times 100 \approx 4.84\%$

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b) Step1: Probability of purple first

$\text{P(purple)} = \frac{14}{32} = \frac{7}{16}$

b) Step2: Probability of green (no replacement)

Total crayons now = 31, so $\text{P(green)} = \frac{4}{31}$

b) Step3: Multiply the two probabilities

$\text{P(purple then green)} = \frac{7}{16} \times \frac{4}{31} = \frac{28}{496} = \frac{7}{124}$

b) Step4: Convert to percentage

$\frac{7}{124} \times 100 \approx 5.65\%$

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c) Step1: Probability of first red

$\text{P(red 1)} = \frac{8}{32} = \frac{1}{4}$

c) Step2: Probability of second red (no replacement)

Total crayons now = 31, red left =7, so $\text{P(red 2)} = \frac{7}{31}$

c) Step3: Multiply the two probabilities

$\text{P(two reds)} = \frac{1}{4} \times \frac{7}{31} = \frac{7}{124}$

c) Step4: Convert to percentage

$\frac{7}{124} \times 100 \approx 5.65\%$

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d) Step1: Probability of first green

$\text{P(green 1)} = \frac{4}{32} = \frac{1}{8}$

d) Step2: Probability of second green (no replacement)

Total crayons now =31, green left=3, so $\text{P(green 2)} = \frac{3}{31}$

d) Step3: Multiply the two probabilities

$\text{P(two greens)} = \frac{1}{8} \times \frac{3}{31} = \frac{3}{248}$

d) Step4: Convert to percentage

$\frac{3}{248} \times 100 \approx 1.21\%$

Answer:

a) Fraction: $\frac{3}{62}$, Percentage: $\approx 4.84\%$
b) Fraction: $\frac{7}{124}$, Percentage: $\approx 5.65\%$
c) Fraction: $\frac{7}{124}$, Percentage: $\approx 5.65\%$
d) Fraction: $\frac{3}{248}$, Percentage: $\approx 1.21\%$