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 .
(round to three decimal places as needed.)

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  .
(round to three decimal places as needed.)

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "blank_filling_formatter", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": false, "concepts_used": [ "Independent Events Probability", "Complementary Events", "At Least One Probability" ], "new_concepts": [], "current_concepts": [ "Independent Events Probability", "Complementary Events", "At Least One Probability" ] } ## Define the given parameters Using the *Independent Events Probability* knowledge point $$ \begin{aligned} &n = 3 \quad \text{(sample size of unrelated people)}\ &p = 0.10 \quad \text{(probability of having type } \text{B}^+ \text{ blood)} \end{aligned} $$ ## Calculate the probability that all three have type B+ blood Using the *Independent Events Probability* knowledge point $$ \begin{aligned} P(\text{All three}) &= p^3 \ &= (0.10)^3 \ &= 0.001000 \quad \text{(rounded to six decimal places)} \end{aligned} $$ ## Calculate the probability that none of the three have type B+ blood Using the *Complementary Events* and *Independent Events Probability* knowledge points $$ \begin{aligned} q &= 1 - p = 1 - 0.10 = 0.90 \ P(\text{None}) &= q^3 \ &= (0.90)^3 \ &= 0.729 \quad \text{(rounded to three decimal places)} \end{aligned} $$ ## Calculate the probability that at least one has type B+ blood Using the *At Least One Probability* and *Complementary Events* knowledge points $$ \begin{aligned} P(\text{At least one}) &= 1 - P(\text{None}) \ &= 1 - 0.729 \ &= 0.271 \quad \text{(rounded to three decimal places)} \end{aligned} $$ (c) Find the probability that at least one of the three has type $\text{B}^+$ blood. The probability that at least one of the three has type $\text{B}^+$ blood is 0.271 (Round to three decimal places as needed.) { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Statistics", "At Least One Probability" ] }

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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

Answer: