the probability that a person in the united states has type $b^+$ blood is 10%. three unrelated people in the united states are selected at random. complete parts (a) through (d).

(a) find the probability that all three have type $b^+$ blood.
the probability that all three have type $b^+$ blood is 0.001.
(round to six decimal places as needed.)

(b) find the probability that none of the three have type $b^+$ blood.
the probability that none of the three have type $b^+$ blood is 0.729.
(round to three decimal places as needed.)

(c) find the probability that at least one of the three has type $b^+$ blood.
the probability that at least one of the three has type $b^+$ blood is 0.271.
(round to three decimal places as needed.)

(d) which of the events can be considered unusual? explain. select all that apply.

a. the event in part (b) is unusual because its probability is less than or equal to 0.05.
b. the event in part (c) is unusual because its probability is less than or equal to 0.05.
c. none of these events are unusual.
d. the event in part (a) is unusual because its probability is less than or equal to 0.05.

Question

the probability that a person in the united states has type $b^+$ blood is 10%. three unrelated people in the united states are selected at random. complete parts (a) through (d).

(a) find the probability that all three have type $b^+$ blood.
the probability that all three have type $b^+$ blood is 0.001.
(round to six decimal places as needed.)

(b) find the probability that none of the three have type $b^+$ blood.
the probability that none of the three have type $b^+$ blood is 0.729.
(round to three decimal places as needed.)

(c) find the probability that at least one of the three has type $b^+$ blood.
the probability that at least one of the three has type $b^+$ blood is 0.271.
(round to three decimal places as needed.)

(d) which of the events can be considered unusual? explain. select all that apply.

a. the event in part (b) is unusual because its probability is less than or equal to 0.05.
b. the event in part (c) is unusual because its probability is less than or equal to 0.05.
c. none of these events are unusual.
d. the event in part (a) is unusual because its probability is less than or equal to 0.05.

Accepted Answer

{ "quality": "clear", "question_count": 4, "skills_matched": [ "step_cot", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": false, "concepts_used": [ "Independent Events Probability", "Complementary Events", "At Least One Probability", "Unusual Event Probability" ], "new_concepts": [], "current_concepts": [ "Independent Events Probability", "Complementary Events", "At Least One Probability", "Unusual Event Probability" ] } ## Define the given parameters Using the *Independent Events Probability* knowledge point $$ \begin{aligned} &P(B^+) = 0.10\ &n = 3 \text{ (independent trials)} \end{aligned} $$ ## Calculate the probability that all three have type B+ blood Using the *Independent Events Probability* knowledge point $$ \begin{aligned} P(\text{all three}) &= (P(B^+))^3 \ &= (0.10)^3 \ &= 0.001000 \end{aligned} $$ ## Calculate the probability that none of the three have type B+ blood Using the *Complementary Events* and *Independent Events Probability* knowledge points $$ \begin{aligned} P(\text{not } B^+) &= 1 - 0.10 = 0.90\ P(\text{none}) &= (P(\text{not } B^+))^3 \ &= (0.90)^3 \ &= 0.729 \end{aligned} $$ ## Calculate the probability that at least one has type B+ blood Using the *At Least One Probability* and *Complementary Events* knowledge points $$ \begin{aligned} P(\text{at least one}) &= 1 - P(\text{none}) \ &= 1 - 0.729 \ &= 0.271 \end{aligned} $$ ## Identify unusual events Using the *Unusual Event Probability* knowledge point $$ \begin{aligned} &\text{An event is unusual if } P(\text{event}) \le 0.05.\ &P(\text{part a}) = 0.001 \le 0.05 \quad (\text{Unusual})\ &P(\text{part b}) = 0.729 > 0.05 \quad (\text{Not unusual})\ &P(\text{part c}) = 0.271 > 0.05 \quad (\text{Not unusual}) \end{aligned} $$ ## Question 1 The probability that all three have type $B^+$ blood is 0.001000. ## Question 2 The probability that none of the three have type $B^+$ blood is 0.729. ## Question 3 The probability that at least one of the three has type $B^+$ blood is 0.271. ## Question 4 A. The event in part (b) is unusual because its probability is less than or equal to 0.05.

B. The event in part (c) is unusual because its probability is less than or equal to 0.05.

C. None of these events are unusual.

D. The event in part (a) is unusual because its probability is less than or equal to 0.05.

{ "subject": "Mathematics", "question_type": "Multi-part", "knowledge_point": [ "Mathematics", "Statistics", "Probability Rules" ] }

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QUESTION IMAGE

Question

Explanation:

Define the given parameters

Calculate the probability that all three have type B+ blood

Calculate the probability that none of the three have type B+ blood

Calculate the probability that at least one has type B+ blood

Identify unusual events

Answer:

Question 1

Question 2

Question 3

Question 4