Question

the responses of 1001 adults in a certain region to a survey question about the story of britons vote to leave the european union are shown in the accompanying pareto chart. find the probability of each event listed in parts (a) through (d) below.

(a) randomly selecting an adult who thinks the story is somewhat important
the probability is 0.319.
(type an integer or a decimal. round to three decimal places as needed.)

(b) randomly selecting an adult who thinks the story is not at all important
the probability is 0.139.
(type an integer or a decimal. round to three decimal places as needed.)

(c) randomly selecting an adult who thinks the story is not too important or not at all important
the probability is
(type an integer or a decimal. round to three decimal places as needed.)

Explanation:

Identify the given values and target

Using the Empirical Probability knowledge point

• Total number of adults surveyed: \(N = 1001\)
• Target event: Randomly selecting an adult who thinks the story is "not too important" or "not at all important".
• From the Pareto chart and key:
• "Not too important" corresponds to response category D, with frequency \(f_D = 201\).
• "Not at all important" corresponds to response category E, with frequency \(f_E = 139\).

Apply the addition rule for mutually exclusive events

Using the Addition Rule for Probability and Mutually Exclusive Events knowledge points

• Since an individual can only choose one response, these two categories are mutually exclusive.
• The combined frequency for the two categories is:

$$ f_{\text{combined}} = f_D + f_E = 201 + 139 = 340 $$

Calculate the empirical probability

Using the Empirical Probability knowledge point

• The probability \(P\) of the combined event is:

$$ P = \frac{f_{\text{combined}}}{N} = \frac{340}{1001} $$

• Performing the division:

$$ P \approx 0.33966 $$

Round to three decimal places

Using the Empirical Probability knowledge point

• Rounding \(0.33966\) to three decimal places yields:

$$ P \approx 0.340 $$

Answer:

(c) Randomly selecting an adult who thinks the story is not too important or not at all important

The probability is <blank>0.340</blank>