Relative And Expected Frequencies (Copy)
1.
A coin is tossed 200 times and lands heads 120 times. Estimate P(Head).
2.
From Q1, estimate P(Tail).
3.
A die is rolled 60 times. A “4” occurs 12 times. Estimate P(rolling a 4).
4.
From Q3, estimate how many times a “4” would appear if the die is rolled 300 times.
5.
A spinner is spun 50 times with outcomes: A=15, B=20, C=15. Estimate P(B).
6.
From Q5, estimate the expected number of times C appears in 200 spins.
7.
A biased coin is tossed 100 times and shows heads 73 times. Estimate P(Head).
8.
From Q7, if the coin is tossed 500 times, how many tails would you expect?
9.
A bag of sweets: frequencies from 80 trials: Red=20, Blue=30, Green=30. Estimate P(Green).
10.
From Q9, if 400 sweets are chosen, how many are expected to be red?
11.
A factory produces bulbs. Out of 1000 tested, 15 were faulty. Estimate P(faulty).
12.
From Q11, how many faulty bulbs expected in 5000 produced?
13.
A survey of 200 people: 140 prefer tea, 60 prefer coffee. Estimate P(tea).
14.
From Q13, estimate how many out of 500 would prefer coffee.
15.
A biased die is rolled 120 times. Outcomes: 1=10, 2=20, 3=30, 4=25, 5=15, 6=20. Which number is most likely to appear?
16.
From Q15, estimate P(rolling a 3).
17.
From Q15, how many times is “6” expected in 600 rolls?
18.
In 100 trials with a spinner, result “Blue” occurred 28 times. Estimate P(Blue).
19.
From Q18, in 350 trials, how many Blues expected?
20.
In 60 rolls of a die, even numbers occurred 38 times. Estimate P(even).
21.
From Q20, if die rolled 300 times, expected number of even outcomes?
22.
A biased spinner has probabilities estimated from trials: A=0.4, B=0.35, C=0.25. In 200 spins, expected number of B?
23.
From Q22, expected number of A?
24.
In 400 spins of a spinner, the frequencies are: Red=110, Blue=150, Yellow=140. Estimate P(Yellow).
25.
From Q24, in 1000 spins, expected number of Blue?
26.
In 50 trials of a coin, results: Head=35, Tail=15. Is the coin fair? Explain using probabilities.
27.
A biased die gives results in 200 rolls: “5” appears 60 times. Estimate P(5).
28.
From Q27, in 1000 rolls, expected number of 5s?
29.
A survey of 600 people: 420 own a smartphone. Estimate P(owning smartphone).
30.
From Q29, in a group of 250 people, how many would you expect to own a smartphone?
1.
P(Head) = 120 ÷ 200 = 0.6.
Relative frequency = frequency ÷ total trials.
2.
P(Tail) = 1 − 0.6 = 0.4.
3.
P(4) = 12 ÷ 60 = 0.2.
4.
Expected 4s = 0.2 × 300 = 60.
5.
P(B) = 20 ÷ 50 = 0.4.
6.
P(C) = 15 ÷ 50 = 0.3.
Expected in 200 spins = 0.3 × 200 = 60.
7.
P(Head) = 73 ÷ 100 = 0.73.
8.
P(Tail) = 1 − 0.73 = 0.27.
Expected Tails = 0.27 × 500 = 135.
9.
P(Green) = 30 ÷ 80 = 0.375.
10.
P(Red) = 20 ÷ 80 = 0.25.
Expected Reds in 400 = 0.25 × 400 = 100.
11.
P(faulty) = 15 ÷ 1000 = 0.015.
12.
Expected faulty = 0.015 × 5000 = 75.
13.
P(tea) = 140 ÷ 200 = 0.7.
14.
P(coffee) = 0.3.
Expected in 500 = 0.3 × 500 = 150.
15.
Highest frequency is “3” (30).
So 3 is most likely.
16.
P(3) = 30 ÷ 120 = 0.25.
17.
P(6) = 20 ÷ 120 = 0.167.
Expected = 0.167 × 600 ≈ 100.
18.
P(Blue) = 28 ÷ 100 = 0.28.
19.
Expected = 0.28 × 350 = 98.
20.
P(even) = 38 ÷ 60 ≈ 0.633.
21.
Expected = 0.633 × 300 ≈ 190.
22.
Expected B = 0.35 × 200 = 70.
23.
Expected A = 0.4 × 200 = 80.
24.
P(Yellow) = 140 ÷ 400 = 0.35.
25.
P(Blue) = 150 ÷ 400 = 0.375.
Expected in 1000 = 0.375 × 1000 = 375.
26.
P(Head) = 35 ÷ 50 = 0.7.
P(Tail) = 0.3.
Not equal → coin not fair. A fair coin should give about 0.5 each.
27.
P(5) = 60 ÷ 200 = 0.3.
28.
Expected 5s = 0.3 × 1000 = 300.
29.
P(smartphone) = 420 ÷ 600 = 0.7.
30.
Expected = 0.7 × 250 = 175.