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 2d 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 / RB / 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 blued 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 / 108 / 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 / trainNumber 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
3
10
1
10
1 1 2
10 2 5
2 a 1 1
1 2 2
3 3 3
1
30
1
30
8
15
8 2 1
15 5 5
1
10
1
20
1
4
9 1
20 4
9
20
1 1
10 5
3
5
d 0 e 2
1
10
3
10
23
31
5
22
8 a 35 b 0.3
9 a 35
41
156
25
39