1) There are twelve marbles in a bag. Five are red with each one numbered from 1

Question

1) There are twelve marbles in a bag. Five are red with each one numbered from 1 to 5, three are blue numbered 1 to 3, four are green numbered 1 to 4 . If one marble is selected at random, what is the probability:

a. it has the number 4 on it.

b. it is red?

c. it does not have the number 1 on it?

d. it is green, given it has the number 2 on it?

e. it has the number 2 on it or the number 4?

f. it has the number 4 on it, given it is red?

g. it is red and had the number 3 on it?

h. it is green, given it has the number 5 on it?

Explanation / Answer

a)

There are 2 marbles out of 12 that has 4 on it. Hence,

P = 2/12 = 1/6 or 0.1666666667 [ANSWER]

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b)

There are 5 reds. Hence,

P = 5/12 [ANSWER]

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c)

There are 3 1s here, and 9 without 1s. Hence,

P = 9/12 = 3/4 [ANSWER]

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d)

There are 3 2s here, 1 of them is green. Hence,

P(green|2) = 1/3 [ANSWER]

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e)

There are 3 2s, and 2 4s. 5 in total. Hence,

P = 5/12 [ANSWER]

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f)

There are 5 reds. Hence,

P = 1/5 [ANSWER]

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g)

There is only 1 red 3. Hence,

P = 1/12 [ANSWER]

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h)

There is no green 5. Hence, this is impossible,

P = 0 [ANSWER]

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