Concept explainers
(a)
To find: The
To obtain: The probability of blue eyes.
To evaluate: The probability of freckles.
To describe: The obtained probabilities in plain English.
(a)

Answer to Problem 13.40E
The probability of red hair is 0.0251.
The probability of blue eyes is 0.3876.
The probability of freckles is 0.00011.
There are 2.51% of children are with red hair.
Among the four different hair colors and three different eye colors of Caucasian child, there are 38.76% chances that a child has blue eyes.
Among the four different hair colors and three different eye colors of Caucasian child, there are 0.011% chances that a child has freckles.
Explanation of Solution
Given info:
The tree diagram shows the effect of eye color, hair color and freckles on the reported extent of burning from sun. The last two braches represent “Freckles and No Freckles” categories for each category.
Calculation:
The probability of red hair is obtained below:
Thus, the probability of red hair is 0.0251.
Interpretation:
Among the four different hair colors (black, brown, blonde, and red) of Caucasian child, there are 2.51% chances that a child has red hair.
Probability of blue eyes:
From the tree diagram,
Hence,
Thus, the probability of blue eyes is 0.3876.
Interpretation:
Among the four different hair colors (black, brown, blonde, and red) and three different eye colors (blue, green, and brown) of Caucasian child, there are 38.77% chances that a child has blue eyes.
The probability of freckles is obtained below:
From the tree diagram,
Thus, the probability of freckles is 0.00011.
Interpretation:
Among the four different hair colors (black, brown, blonde, and red) and three different eye colors (blue, green, and brown) of Caucasian child, there are 12.48% chances that a child has freckles.
(b)
To find: The probability of freckles and red hair.
To evaluate: The conditional probability of freckles given that red hair.
(b)

Answer to Problem 13.40E
The probability of freckles and red hair is 0.0203.
The probability of freckles given that hair is red is 0.8088.
Explanation of Solution
Calculation:
From the Tree diagram of children of Caucasian descent, the required probability is,
Thus, the probability of freckles and red hair is 0.0203.
Interpretation:
Among the freckles and no freckles with red hair of Caucasian child, there are 2.03% chances that a child has freckles and red hair.
The conditional probability of freckles given that red hair:
From the tree diagram of children of Caucasian descent, the required probability is,
Thus, the conditional probability of freckles given that hair is red is 0.8088.
Interpretation:
Among the freckles with red hair of Caucasian child, there are 80.88% chances that a child has freckles given red hair.
(c)
To check: Whether the
(c)

Answer to Problem 13.40E
The events “freckles” and “red hair” are not independent.
Explanation of Solution
The probability of freckles is 0.00011 and the probability of red hair is 0.0251. Also, the probability of freckles and red hair is 0.0203.
Hence,
Thus, the events “freckles” and “red hair” are not independent.
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Chapter 13 Solutions
BASIC PRACTICE OF STATISTICS >C<
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