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At a science museum, visitors can compete to see who has a faster reaction time. Competitors watch a red screen, and the moment they see it turn from red to green, they push a button. The machine records their reaction times and also asks competitors to report their gender. $\newline$ The probability that a competitor reacted in over $0.7$ seconds is $0.6$ , the probability that a competitor was female is $0.4$ , and the probability that a competitor reacted in over $0.7$ seconds and was female is $0.3$ . $\newline$ What is the probability that a randomly chosen competitor reacted in over $0.7$ seconds or was female? $\newline$ Write your answer as a whole number, decimal, or simplified fraction. $\newline$ ______

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Find probabilities using the addition rule

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Q. At a science museum, visitors can compete to see who has a faster reaction time. Competitors watch a red screen, and the moment they see it turn from red to green, they push a button. The machine records their reaction times and also asks competitors to report their gender.

\newline

The probability that a competitor reacted in over

0.7

seconds is

0.6

, the probability that a competitor was female is

0.4

, and the probability that a competitor reacted in over

0.7

seconds and was female is

0.3

.

\newline

What is the probability that a randomly chosen competitor reacted in over

0.7

seconds or was female?

\newline

Write your answer as a whole number, decimal, or simplified fraction.

\newline

______

Identify Probabilities: To find the probability that a randomly chosen competitor reacted in over `0.7` seconds or was female, we can use the formula for the probability of the union of two events `A` and `B,` which is `P(text(A ∪ B)) = P(text(A)) + P(text(B)) - P(text(A ∩ B))`. Here, event `A` is the competitor reacting in over `0.7` seconds, and event `B` is the competitor being female.
Apply Formula: First, we identify the probabilities given:`P(text(A)) =` Probability that a competitor reacted in over `0.7` seconds `= 0.6``P(text(B)) =` Probability that a competitor was female `= 0.4``P(text(A ∩ B)) =` Probability that a competitor reacted in over `0.7` seconds and was female `= 0.3
Perform` Calculation: Now, we apply the formula to find `P(text(A ∪ B)):``P(text(A ∪ B)) = P(text(A)) + P(text(B)) - P(text(A ∩ B))``P(text(A ∪ B)) = 0.6 + 0.4 - 0.3
Final` Probability: We perform the calculation:`P(text(A ∪ B)) = 0.6 + 0.4 - 0.3``P(text(A ∪ B)) = 1.0 - 0.3``P(text(A ∪ B)) = 0.7
The` probability that a randomly chosen competitor reacted in over `0.7` seconds or was female is `0.7.

`

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