Exercise 9 Page 697

We are performing an experiment to determine how well plants grow under different light sources. Out of 30 plants in the experiment, 12 receive visible light, 15 receive ultraviolet light, and 6 receive both visible and ultraviolet light. We want to find the probability that the plant receives visible or ultraviolet light. Recall the formula for probability of compound events. P(AorB)=P(A)+P(B)-P(AandB)

We can mark the event of receiving visible light as A and the event of receiving ultraviolet light as B. To calculate the needed probabilities we need to divide the number of favorable outcomes for every event by the total number of possible outcomes, 30. Recall that 12 plants received visible light, 15 received ultraviolet light, and 6 received both.

Event	Favorable Outcomes	Probability
A	B	A and B
12	15	6
12/30	15/30	6/30

Now we can substitute the obtained probabilities into the formula for the probability of compound events and find the value of P(AorB). Let's do it!

P(AorB)=P(A)+P(B)-P(AandB)

SubstituteValues

Substitute values

P(AorB)=12/30+15/30-6/30

AddSubFrac

Add and subtract fractions

P(AorB)=21/30

ReduceFrac

a/b=.a /3./.b /3.

P(AorB)=7/10

The probability that the plant in the experiment receives visible or ultraviolet light is 710, or 0.7.