A sociology teacher asked her students to complete a survey at the beginning of the year. One survey question asked, "Are you responsible?" Another question asked, "How many siblings do you have?"The probability that a student is irresponsible is 0.4, the probability that a student has 0 siblings is 0.5, and the probability that a student is irresponsible and has 0 siblings is 0.3.What is the probability that a randomly chosen student is irresponsible or has 0 siblings?Write your answer as a whole number, decimal, or simplified fraction.
Question
A sociology teacher asked her students to complete a survey at the beginning of the year. One survey question asked, "Are you responsible?" Another question asked, "How many siblings do you have?"The probability that a student is irresponsible is 0.4, the probability that a student has 0 siblings is 0.5, and the probability that a student is irresponsible and has 0 siblings is 0.3.What is the probability that a randomly chosen student is irresponsible or has 0 siblings?Write your answer as a whole number, decimal, or simplified fraction.
Solution 1
The probability that a student is irresponsible or has 0 siblings can be found using the formula for the probability of the union of two events: P(A or B) = P(A) + P(B) - P(A and B).
Here, event A is the student being irresponsible and event B is the student having 0 siblings.
P(A) = Probability that a student is irresponsible = 0.4 P(B) = Probability that a student has 0 siblings = 0.5 P(A and B) = Probability that a student is irresponsible and has 0 siblings = 0.3
Substituting these values into the formula gives:
P(A or B) = P(A) + P(B) - P(A and B) = 0.4 + 0.5 - 0.3 = 0.6
So, the probability that a randomly chosen student is irresponsible or has 0 siblings is 0.6.
Solution 2
The probability that a student is irresponsible or has 0 siblings can be found using the formula for the probability of the union of two events: P(A or B) = P(A) + P(B) - P(A and B).
Here, event A is the student being irresponsible and event B is the student having 0 siblings.
P(A) = Probability that a student is irresponsible = 0.4 P(B) = Probability that a student has 0 siblings = 0.5 P(A and B) = Probability that a student is irresponsible and has 0 siblings = 0.3
Substituting these values into the formula gives:
P(A or B) = P(A) + P(B) - P(A and B) = 0.4 + 0.5 - 0.3 = 0.6
So, the probability that a randomly chosen student is irresponsible or has 0 siblings is 0.6.
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