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The sample space listing the eight simple events that are possible when a couple has three children is​ {bbb, bbg,​ bgb, bgg,​ gbb, gbg,​ ggb, ggg}. After identifying the sample space for a couple having four​ children, find the probability of getting three girls and one boy (in any order ).

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amna04352

Answer:

¼

Step-by-step explanation:

BBBB

GGGG

BBBG

BBGB

BGBB

GBBB

GGGB

GGBG

GBGG

BGGG

BBGG

GGBB

GBGB

BGBG

GBBG

BGGB

3G and 1B

4/16 = 1/4

Using probability and sample space concepts, it is found that there is a 0.25 = 25% probability of getting three girls and one boy (in any order ).

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  • The sample space is the set that contains all possible outcomes.
  • A probability, calculated from a sample space, is the number of desired outcomes in the sample space divided by the number of total outcomes.

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For 4 children, the sample space is given by:

B - B - B - B

B - B - B - G

B - B - G - B

B - B - G - G

B - G - B - B

B - G - B - G

B - G - G - B

B - G - G - G

G - B - B - B

G - B - B - G

G - B - G - B

G - B - G - G

G - G - B - B

G - G - B - G

G - G - G - B

G - G - G - G

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  • There are 16 outcomes.
  • In 4, that are B-G-G-G, G-B-G-G, G-G-B-G and G-G-G-B, there are 3 girls and one boy.

Thus:

[tex]p = \frac{D}{T} = \frac{4}{16} = 0.25[/tex]

0.25 = 25% probability of getting three girls and one boy (in any order ).

A similar problem is given at https://brainly.com/question/16256175

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