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Core Connections Integrated II, 2015

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Core Connections Integrated II, 2015 View details

1. Section 7.1

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Exercise 30 Page 382

Practice makes perfect

a To calculate the probability of two events happening, we have to use the Multiplication Rule of Probability.

P(A and B)=P(A)* P(B) From the exercise, we know that the probability of landing on heads is 0.8. Now we can calculate the probability that Earl will have to do both chores. In other words, we can find the probability that he lands on heads twice.

P(A and B)=P(A)* P(B)

P(A)= 0.8, P(B)= 0.8

P(both)=( 0.8)( 0.8)

Multiply

P(both)=0.64

Convert to percent

P(both)=64 %

b Let's illustrate the different outcomes with a tree diagram. Assume that the first coin toss decides whether or not Earl has to take out the garbage. The second toss decides if he needs to do the dishes. The highlighted path shows the outcome that results in garbage duty but no need to wash the dishes.

Again, to calculate the probability of this event, we have to use the Multiplication Rule of Probability.

P(A and B)=P(A)* P(B)

SubstituteValues

Substitute values

P(garbage, no dishes)= 0.8* 0.2

Multiply

P(garbage, no dishes)=0.16

Convert to percent

P(garbage, no dishes)=16 %

There is a 16 % probability that Earl will not have to take out the garbage but will have to do the dishes.

Subchapter links

7.1.1 Explore–Conjecture–Prove p.376-379

7.1.2 Properties of Rhombi p.382-383

7.1.3 Two-Column Proofs p.387-388

7.1.4 More Geometric Proofs p.390-391

7.1.5 Using Similar Triangles to Prove Theorems p.395-396