1 a Six-Sided Die Is Rolled 20 Times and the Results Are Shown Below

Experimental probabilities

1 A six-sided die is rolled 20 times and the results are shown below: 6, 6, 1, 4, 3, 5, 1, 3, 6, 2, 5, 6, 2, 3, 1, 6, 1, 1, 4, 6 From these results, find the estimated probability of rolling:

a a 6 6/20 = 3/10 b a 4 c a 2 d an odd number e a number more than 4

2 A spinner has sections marked in blue, red and green. The spinner is spun 30 times and the results are shown below:

G G R B B B R R G R G R G B R

B G G B B B G G R B G B R R R

From these results, find the estimated probability of spinning:

a green b red c blue d not blue e green or blue

3 A ten-sided die is rolled 30 times and the results are shown below:

3 3 2 1 8 1 5 4 10 1 9 7 3 3 10

8 4 3 10 10 1 2 7 10 4 1 10 2 4 2

From these results, find the estimated probability of rolling:

a a 5 b a 9

c an even number d a number greater than 3

e a prime number f a multiple of 3

4 A coin is tossed and then a die is rolled. The outcomes of 20 trials are shown below: H2, H6, T3, H4, T4, H1, H1, H5, T5, T6, H3, T1, H3, T6, T5, T4, H4, T6, T5, T5 From these results, find the estimated probability of obtaining:

a a head and a 4 b a tail and a 1

c a tail and an even number d a head

e a 5 f a tail and a number greater than 3 5 A bag contains counters numbered 1, 2, 3, 4 and 5. A counter is removed and is not replaced, then a second counter is removed. The outcome expressed as (3, 2) represents selecting a 3 on the first draw and a 2 on the second draw. The results of 20 trials are shown below: (3, 2) (2, 4) (5, 1) (1, 3) (2, 5) (5, 3) (3, 2) (4, 5) (4, 3) (5, 4) (2, 3) (5, 2) (4, 3) (2, 1) (2, 4) (1, 4) (1, 3) (2, 1) (5, 2) (6, 3) From these results, find the estimated probability of obtaining:

a a 3 on the first draw

b a 4 on the second draw

c a first number that is greater than the second number drawn

d a first number that is the same as the second number drawn

e a first number that is less than the second number drawn

f an even number for both draws

g a first number that is odd and a second number that is even

6 Ballarat has an average of eight sunny days in July. Find the estimated probability that, in Ballarat in the month of July, it is not sunny.

7 In a Year 7 class, 17 out of 22 students have a mobile phone. Find the probability that a student in this class does not have a mobile phone.

8 A survey of 50 people at the local shopping centre found that 70% of people eat fruit at least once a day. Find:

a the number of the people questioned who eat fruit at least once each day

b the probability that a person questioned does not eat fruit once each day.

9 A survey is conducted to determine how students travelled to school. The results obtained are shown below.

Type of transport car bicycle walk bus train

Number of students 25 41 15 70 5

From the results, find the estimated probability that a student travelled to school by:

a bus b bicycle c car, bus or train Answers

1 1 1 2 3 10 10 2 5 10

1 1 2 2 2 a 3 3 3

1 1 8 8 2 1 30 30 15 15 5 5

1 29 9 0 0

1 d 3 10 1 10

8 a 35

25 9 4 39 1 1 5 6