Question

Basket A has has 5 pink marbles and 3 orange marbles. Basket B has 4 pink marbles and 2 orange marbles. One marble is chosen at random from each basket. find the probability that

a) both marbles are pink

b) both marbles are NOT pink

c) exactly ONE marble is pink

Answer 1

Answer 2

Solution:

Given:

• Basket A: 5 pink marbles and 3 orange marbles.

• Basket B: 4 pink marbles and 2 orange marbles.

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a) Probability that both marbles are pink:

$$P(\text{Pink from A})=\frac{5}{8},P(\text{Pink from B})=\frac{4}{6}=\frac{2}{3}$$$$P(\text{Both Pink})=\frac{5}{8}\times \frac{2}{3}=\frac{10}{24}=\frac{5}{12}$$

Answer: $\boxed{{\displaystyle \frac{5}{12}}}$

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b) Probability that both marbles are NOT pink:

$$P(\text{Not Pink from A})=\frac{3}{8},P(\text{Not Pink from B})=\frac{2}{6}=\frac{1}{3}$$$$P(\text{Both Not Pink})=\frac{3}{8}\times \frac{1}{3}=\frac{3}{24}=\frac{1}{8}$$

Answer: $\boxed{{\displaystyle \frac{1}{8}}}$

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c) Probability that exactly ONE marble is pink:

$$P(\text{Pink from A and Not Pink from B})=\frac{5}{8}\times \frac{1}{3}=\frac{5}{24}$$$$P(\text{Not Pink from A and Pink from B})=\frac{3}{8}\times \frac{2}{3}=\frac{6}{24}=\frac{1}{4}$$$$P(\text{Exactly One Pink})=\frac{5}{24}+\frac{1}{4}=\frac{5}{24}+\frac{6}{24}=\frac{11}{24}$$

Answer: $\boxed{{\displaystyle \frac{11}{24}}}$

Answer 3

Let's break down this probability problem step-by-step:

Basket A:

• 5 pink marbles

• 3 orange marbles

• Total: 8 marbles

Basket B:

• 4 pink marbles

• 2 orange marbles

• Total: 6 marbles

a) Probability that both marbles are pink

• Probability of picking a pink marble from Basket A: 5/8

• Probability of picking a pink marble from Basket B: 4/6 = 2/3

Since the events are independent (choosing from each basket doesn't affect the other), we multiply the probabilities:

• Probability (both pink) = (5/8) * (2/3) = 10/24 = 5/12

b) Probability that both marbles are NOT pink (both orange)

• Probability of picking an orange marble from Basket A: 3/8

• Probability of picking an orange marble from Basket B: 2/6 = 1/3

Multiply the probabilities:

• Probability (both orange) = (3/8) * (1/3) = 3/24 = 1/8

c) Probability that exactly ONE marble is pink

There are two scenarios:

• Scenario 1: Pink from A, Orange from B

• Probability (Pink from A): 5/8

• Probability (Orange from B): 2/6 = 1/3

• Probability (Pink from A, Orange from B) = (5/8) * (1/3) = 5/24

• Scenario 2: Orange from A, Pink from B

• Probability (Orange from A): 3/8

• Probability (Pink from B): 4/6 = 2/3

• Probability (Orange from A, Pink from B) = (3/8) * (2/3) = 6/24 = 1/4

Since these are mutually exclusive events (they can't both happen at the same time), we add the probabilities:

• Probability (Exactly one pink) = 5/24 + 1/4 = 5/24 + 6/24 = 11/24

Answers:

a) Probability that both marbles are pink: 5/12

b) Probability that both marbles are NOT pink: 1/8

c) Probability that exactly ONE marble is pink: 11/24