Question

the responses of 940 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.
click the icon to view the pareto chart.
(a) randomly selecting an adult who thinks the story is somewhat important
the probability is
(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
(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.)
(d) randomly selecting an adult who thinks the story is extremely important or very important
the probability is
(type an integer or a decimal. round to three decimal places as needed.)

Explanation:

Step1: Calculate total number of adults

Total number of adults \(n = 325+206 + 183+108+96+22=940\)

Step2: Calculate probability for part (a)

Number of adults who think story is somewhat important \(n_C=325\). Probability \(P(C)=\frac{n_C}{n}=\frac{325}{940}\approx0.346\)

Step3: Calculate probability for part (b)

Number of adults who think story is not at all important \(n_E = 108\). Probability \(P(E)=\frac{n_E}{n}=\frac{108}{940}\approx0.115\)

Step4: Calculate probability for part (c)

Number of adults who think story is not too important \(n_D = 183\) and not at all important \(n_E=108\). Total \(n_{D\cup E}=183 + 108=291\). Probability \(P(D\cup E)=\frac{n_{D\cup E}}{n}=\frac{291}{940}\approx0.309\)

Step5: Calculate probability for part (d)

Number of adults who think story is extremely important \(n_A=96\) and very important \(n_B = 206\). Total \(n_{A\cup B}=96+206=302\). Probability \(P(A\cup B)=\frac{n_{A\cup B}}{n}=\frac{302}{940}\approx0.321\)

Answer:

(a) \(0.346\)
(b) \(0.115\)
(c) \(0.309\)
(d) \(0.321\)