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Svetach [21]
3 years ago
9

A bag contains 4 red marbles, 6 blue marbles and 7 green marbles. If three marbles are drawn out of the bag, what is the probabi

lity, to the nearest 1000th, that all three marbles drawn will be green?
Mathematics
1 answer:
yawa3891 [41]3 years ago
3 0

Answer:

Step-by-step explanation:

Total marble = 4+6+7 = 17

Number of green = 7

Prob(1st green) = 7/17

Now their are 6 green left and 16 marble

Prob(2nd green) = 6/16 = 3/8

Now their are 5 green left and 15 marble

Prob(3rd green) = 5/15 = 1/3

Prob(1st and 2nd and 3rd green) will be = 7/17 × 3/8 × 1/3

= 7/(17×8)

= 7/136

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Answer:

(a) See attachment for tree diagram

(b) 24 possible outcomes

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Urn\ 1 = \{B_1, R_1, R_2, R_3\}

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If urn 1 is selected, the following selection exists:

B_1 \to [R_1, R_2, R_3]; R_1 \to [B_1, R_2, R_3]; R_2 \to [B_1, R_1, R_3]; R_3 \to [B_1, R_1, R_2]

If urn 2 is selected, the following selection exists:

B_2 \to [B_3, R_4, R_5]; B_3 \to [B_2, R_4, R_5]; R_4 \to [B_2, B_3, R_5]; R_5 \to [B_2, B_3, R_4]

<em>See attachment for possibility tree</em>

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<u>For urn 1</u>

There are 4 balls in urn 1

n = \{B_1,R_1,R_2,R_3\}

Each of the balls has 3 subsets. i.e.

B_1 \to [R_1, R_2, R_3]; R_1 \to [B_1, R_2, R_3]; R_2 \to [B_1, R_1, R_3]; R_3 \to [B_1, R_1, R_2]

So, the selection is:

Urn\ 1 = 4 * 3

Urn\ 1 = 12

<u>For urn 2</u>

There are 4 balls in urn 2

n = \{B_2,B_3,R_4,R_5\}

Each of the balls has 3 subsets. i.e.

B_2 \to [B_3, R_4, R_5]; B_3 \to [B_2, R_4, R_5]; R_4 \to [B_2, B_3, R_5]; R_5 \to [B_2, B_3, R_4]

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Urn\ 2 = 4 * 3

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Total number of outcomes is:

Total = Urn\ 1 + Urn\ 2

Total = 12 + 12

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