Question

a balloon artist counted the number of balloon animal requests she received at a party. the balloon requests differed in animal type and color. the probability that a balloon animal is blue is 0.5, and the probability that it is shaped like a dinosaur is 0.6. what is the probability that a randomly chosen balloon animal is blue or is shaped like a dinosaur if those are independent events? write your answer as a whole number, decimal, or simplified fraction.

Explanation:

Step1: Recall the formula for independent events

For two independent events \( A \) and \( B \), the probability of \( A \) or \( B \) is given by \( P(A \cup B)=P(A)+P(B)-P(A)P(B) \). Let \( A \) be the event that a balloon animal is blue (\( P(A) = 0.5 \)) and \( B \) be the event that it is shaped like a dinosaur (\( P(B)=0.6 \)).

Step2: Substitute the values into the formula

Substitute \( P(A) = 0.5 \), \( P(B)=0.6 \) into the formula:
\( P(A \cup B)=0.5 + 0.6-(0.5\times0.6) \)
First, calculate the product \( 0.5\times0.6 = 0.3 \).
Then, calculate \( 0.5+0.6 = 1.1 \).
Finally, \( 1.1 - 0.3=0.8 \).

Answer:

\( 0.8 \)