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According to scientific research, the probability that a person between the ages of 20 and 25 having high blood pressure, is only 17 %. In a random survey of 10 people in this age group, what is the probability that two or fewer have high blood pressure?

Respuesta :

Answer:

The probability is [tex]{\frac{83}{100} }^9 \times \frac{17}{100}[/tex] + [tex]{\frac{83}{100} }^8 \times {\frac{17}{100} }^2[/tex] + [tex]{\frac{83}{100} }^{10}[/tex].

Step-by-step explanation:

The probability of having high blood pressure is 17%.

We need to find the probability of 2 or fewer have high blood pressure.

Possibility 1: No one have high blood pressure.

The probability is [tex]{\frac{100 -17}{100} }^{10} = {\frac{83}{100} }^{10}[/tex].

Possibility 2: Only one have high blood pressure.

The probability is [tex]{\frac{83}{100} }^9 \times \frac{17}{100}[/tex].

Possibility 3: 2 among the 10 have the high blood pressure.

[tex]{\frac{83}{100} }^8 \times {\frac{17}{100} }^2[/tex].

Any of the possibilities can happen.

Hence, the required probability is [tex]{\frac{83}{100} }^9 \times \frac{17}{100}[/tex] + [tex]{\frac{83}{100} }^8 \times {\frac{17}{100} }^2[/tex] + [tex]{\frac{83}{100} }^{10}[/tex].

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