** llfJ PROBABILITY TREE DIAGRAMS**

**EXERCISE 4. 12 Probability tree diagrams ••)·ini•iJfJ Rachel is a keen pistol shooter.**

During competitions, the probability that she will hit the target is 0.9.

a What is the probability that Rachel will miss the target in any competition shot? b Rachel fires 2 shots in a competition. Copy

and complete the tree diagram.
**First shot ** **Second shot **

hit fr

hit

0.9 _{� }

miss

miss

c Calculate the probability that Rachel will hit the target with both shots.

d What is the probability that she will miss the target with her first shot and hit it with her second shot?

2 Jayden drives through two sets of traffic lights on his way to school. The probability that the first light is red is 0.5 and the probability that the second light is red is 0.4.

a Copy and complete the missing parts of the probability tree diagram. First light Second light � ,e d

*,ll *

"
d
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b What is the probability that both sets of lights will be red? c Calculate the probability that neither light will be red.

d Determine the probability that Jayden will get a red light followed by a light that isn't red.

3

**Bl·inHGIEi **

In Australia, 7% of adults have a dentist phobia (fear of dentists).
a What is the probability that a randomly selected Australian adult is not afraid of dentists?

b A journalist chooses two adults at random to interview about health issues. Copy and complete the tree diagram.

c Calculate the probability that one of the adults has a dentist phobia but the other doesn't.

d What is the probability that at least one of the adults doesn't have a dentist phobia?

0.07 First person Phobia Second person

4 Every morning on my way to work I turn right through a set of traffic lights that involve a railway crossing.

The probability that I will have to stop at a red light depends upon whether a train is expected. If a train is expected, the probability that I will have to stop is 0.9. If a train is not expected, the probability that I will have to stop is only 0.4. When I am travelling to work, the probability that a train will be expected is 0.15.

a Complete the probability tree diagram.

0.15 train expected train not expected Stop non Stop Stop non Stop

b Calculate the probability that I will have to stop at the traffic lights when I am travelling to work.

c Approximately how many times in 20 trips to work will I have to stop at these traffic lights? 5 Lance is play ing in a soccer competition over the weekend. The probability of rain on Saturday

is 0.25 and Sunday is 0.4.

a Calculate the probability that it will rain on Saturday and Sunday.

b What is the probability that it will rain on only one day over the weekend? c Calculate the probability that it will not rain all weekend.

6 The butcher has a large jar of jelly beans to give to good children. He knows that 60% of the jelly beans in the jar are red. The butcher lets Samir choose two jelly beans from the jar at random. What is the probability that:

a the first jelly bean he chooses is red? b both jelly beans he chooses are red? c at least one of the jelly beans he

When there are a large number of items and we don't

know the number, or the probability is given as a

percentage, we don't have to change the probability for

chooses is red? selecting the second item.

7 Recent TV commercials report that the probability of being tested by a random breath-testing unit late on Friday night is 0.3. On the next two Friday nights, Liam is meeting friends and will be driving home late.

a What is the probability that he won't be random breath-tested on the first Friday night? b What is the probability that he will be random breath-tested at least once on the next two

Friday nights?

8 Sarah and Rhys are about to sit the driving theory test to get their L-plates. The probability that Sarah will pass is 0.8 and the probability that Rhys will pass is 0.6.

a What is the probability that they will both pass the test?

b Calculate the probability that Rhys will pass but Sarah won't. c Calculate the probability that at least one of them will pass.

9 Chloe finds it hard to get out of bed in the morning. On any day, the chance that she will be late to school is 0.3.

a What is the probability that Chloe will be late for school tomorrow and the following day? b Calculate the probability that Chloe will be on time for school on the next two school days. c What is the probability that Chloe will be late for school at least once in the next two days?

**10 ** Research shows that 85% of Australian haemophiliacs lack 'factor 8' in their blood, one of the
factors that makes blood clot. If two Australian haemophiliacs are selected at random, what is
the probability that they both lack 'factor 8' in their blood?

11 Ella has a biased coin that shows tails 60% of the time. a What is the probability that the coin shows heads?

b Ella is going to toss the coin twice. Calculate the probability that she tosses a head and a tail in either order.

12 For cars travelling along the main road late at night, all the traffic lights are green 90% of the time.

a What is the probability that a car travelling on the main road late at night will get a green light at any one set of traffic lights?

b Pauline will drive through two sets of lights when she drives along the main road at midnight. What is the probability that both sets of lights will be green?

c Sylvia is driving along a minor road late at night. The road meets the main road at a set of traffic lights. Explain why the probability that Sylvia will get a green light is only 0.1. Ignore yellow lights.

d There are two sets of traffic lights between Brian's house and his girlfriend's house. At one set oflights, Brian is on a minor road and at the other he is travelling on the main road. When he leaves his girlfriend's house late at night to drive home, what is the probability that he will