### Home > GC > Chapter 6 > Lesson 6.2.2 > Problem6-55

6-55.

Multiple Choice: To decide if his class would take a quiz today, he will flip a coin three times. If all three results are heads or all three results are tails, he will give the quiz. Otherwise, his students will not be tested. What is the probability that his class will take the quiz?

1. $\frac { 1 } { 8 }$

1. $\frac { 1 } { 4 }$

1. $\frac { 1 } { 2 }$

1. $1$

Use a tree diagram to calculate the probability.

For help with the probability models, see Lesson 4.2.4.

Draw the tree diagram one step at a time.

Calculate the probability of three consecutive heads (H) or tails (T).

If you follow the branches of the tree diagram for H, H, H you get the P(H,H,H) by multiplying (0.5)(0.5)(0.5) = 0.125 --> give quiz

If you follow the branches of the tree diagram for T, T, T you get the P(T,T,T) by multiplying (0.5)(0.5)(0.5) = 0.125 --> give quiz

Calculate the probability that the teacher will give the quiz. To do so add the P(H,H,H) + P(T,T,T).

P(give quiz) = 0.125 + 0.125 = 0.25.

B; see response in Step 5 for reason.