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Core Connections Integrated II, 2015

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Core Connections Integrated II, 2015 View details

Chapter Closure

Exercise 120 Page 202

To calculate the probability of two events occurring, you have to multiply their individual probabilities.

P(both)=31.5 %
P(neither)=16.5 %
Probability area model:

The probability of two events both occurring is the product of the individual probabilities. If 45 % of all people have dimples, and 70 % have a widow's peak, we can express this as the following probabilities. P(dimples)&=45/100 [0.8em] P(widow's peak)&=70/100 To calculate the probability of selecting a person with both of these traits, we have to multiply these probabilities.

P(both)=45/100* 70/100

▼

Simplify right-hand side

Multiply fractions

P(both)=3150/10000

a/b=.a /10./.b /10.

P(both)=315/1000

Calculate quotient

P(both)=0.315

Convert to percent

P(both)=31.5 %

Next, we will calculate the probability of selecting a person with neither of the physical traits. If 45 % have dimples, then 55 % do not have dimples. Similarly, if 70 % has a widow's peak, then 30 % does not have a widow's peak. We can write this as the following probabilities. P(no dimples)&=55/100 P(no widow's peak)&=30/100 Again, to calculate the probability of selecting a person with neither of these traits, we have to multiply the individual probabilities.

P(neither)=55/100* 30/100

▼

Simplify right-hand side

Multiply fractions

P(neither)=1650/10000

a/b=.a /10./.b /10.

P(neither)=165/1000

Calculate quotient

P(neither)=0.165

Convert to percent

P(neither)=16.5 %

Let's summarize what we have found. P(both)&=31.5 % P(neither)&=16.5 %

Probability Area Model

To represent this as a probability area model, we have to make sure that the area of the slots assigned to the different combinations corresponds to their respective probabilities. Therefore, we also have to calculate the probability of selecting someone with only dimples and someone with only a widow's peak. P(only widow's peak)&=55/100* 70/100=38.5 % [0.8em] P(only dimples)&=45/100* 30/100=13.5 % With this, we can create a probability area model that represents the situation accurately.

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