Question

in sebastians class, the probability that a randomly selected student has at least one sibling is 0.7. the probability that a randomly selected student has at least one pet is 0.6. the probability that a randomly selected student has at least one sibling and at least one pet is 0.55. what is the probability that a randomly selected student has at least one sibling or at least one pet? write your answer as a decimal. do not round.

Explanation:

Step1: Recall the formula for \(P(A\cup B)\)

The formula for the probability of the union of two events \(A\) and \(B\) is \(P(A\cup B)=P(A)+P(B)-P(A\cap B)\). Let \(A\) be the event that a student has at least one sibling and \(B\) be the event that a student has at least one pet.

Step2: Substitute the given values into the formula

We know that \(P(A) = 0.7\), \(P(B)=0.6\), and \(P(A\cap B)=0.55\). Substituting these values into the formula \(P(A\cup B)=P(A)+P(B)-P(A\cap B)\), we get \(P(A\cup B)=0.7 + 0.6-0.55\).

Step3: Calculate the result

First, add \(0.7\) and \(0.6\): \(0.7+0.6 = 1.3\). Then subtract \(0.55\) from \(1.3\): \(1.3-0.55=0.75\).

Answer:

\(0.75\)