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aivan3 [116]
2 years ago
13

Katrina drinks 0.5 gallons of water per day. Which expression shows how to find the number of cups of water she drinks in a week

?
There are 16 cups in a gallon.

A. 0.5 gallons/1 day × 16 cups/1 gallon × 1 week/7 days
B. 0.5 gallons/1 day × 1 gallon/16 cups × 7 days/1 week
C. 0.5 gallons/1 day × 1 gallon/16 cups × 1 week/7 days
D. 0.5 gallons/1 day × 16 cups/1 gallon × 7 days/1 week
Mathematics
1 answer:
Natali [406]2 years ago
6 0

Answer:

D.

Step-by-step explanation:

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Answer:

(a)\dfrac{92}{117}

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Step-by-step explanation:

Number of Men, n(M)=24

Number of Women, n(W)=3

Total Sample, n(S)=24+3=27

Since you cannot appoint the same person twice, the probabilities are <u>without replacement.</u>

(a)Probability that both appointees are men.

P(MM)=\dfrac{24}{27}X \dfrac{23}{26}=\dfrac{552}{702}\\=\dfrac{92}{117}

(b)Probability that one man and one woman are appointed.

To find the probability that one man and one woman are appointed, this could happen in two ways.

  • A man is appointed first and a woman is appointed next.
  • A woman is appointed first and a man is appointed next.

P(One man and one woman are appointed)=P(MW)+P(WM)

=(\dfrac{24}{27}X \dfrac{3}{26})+(\dfrac{3}{27}X \dfrac{24}{26})\\=\dfrac{72}{702}+\dfrac{72}{702}\\=\dfrac{144}{702}\\=\dfrac{8}{39}

(c)Probability that at least one woman is appointed.

The probability that at least one woman is appointed can occur in three ways.

  • A man is appointed first and a woman is appointed next.
  • A woman is appointed first and a man is appointed next.
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P(at least one woman is appointed)=P(MW)+P(WM)+P(WW)

P(WW)=\dfrac{3}{27}X \dfrac{2}{26}=\dfrac{6}{702}

In Part B, P(MW)+P(WM)=\frac{8}{39}

Therefore:

P(MW)+P(WM)+P(WW)=\dfrac{8}{39}+\dfrac{6}{702}\\$P(at least one woman is appointed)=\dfrac{25}{117}

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