The Legal Aid Committee of a university organised a fundraising fair. One of the attractions was a lucky-draw game. A box contained 40 identical tokens that differed only in colour. There were 12 red tokens, 10 blue tokens, 8 green tokens, 6 yellow tokens and 4 white tokens. Since every token had the same shape and size, each token had an equal chance of being selected. Unless stated otherwise, a token drawn from the box was replaced before the next draw.

The fair also had a spinner divided into eight equal sections numbered from 1 to 8. Since all sections were equal, the probability of the pointer stopping on any particular number was the same. At another counter, participants rolled a standard six-sided die numbered from 1 to 6.

For the final round, a participant had to spin the spinner once and roll the die once. The result of the spinner did not affect the result of the die. Similarly, when a token was selected from the box, the selection was made randomly without looking inside. The committee used these games to teach visitors how probability could help measure the likelihood of uncertain events.

Questions

1. What is the probability of drawing a red token from the box?

A.  3/10

B.  1/4

C.  2/5

D.  3/20

2. What is the probability of drawing either a blue or a green token?

A.  2/5

B.  9/20

C.  1/2

D.  7/20

3. What is the probability of drawing a token that is neither yellow nor white?

A.  1/2

B.  2/5

C.  3/4

D.  4/5

4. If two tokens are drawn successively without replacement, what is the probability that both are white?

A.  1/100

B.  1/130

C.  1/90

D.  2/195

5. In the final round, what is the probability of getting an even number on the spinner and a number greater than 4 on the die?

A.  1/6

B.  1/4

C.  1/3

D.  5/12

Answers and Detailed Explanations

Answer Sequence: A, B, C, B, A

1. Answer: A. 3/10

There are 12 red tokens out of a total of 40 tokens.

P(red token) = Number of red tokens ÷ Total number of tokens

P(red token) = 12/40 = 3/10

Therefore, the probability of drawing a red token is 3/10.

2. Answer: B. 9/20

The box contains 10 blue tokens and 8 green tokens. A selected token cannot be both blue and green, so the favourable outcomes can be added.

Number of blue or green tokens = 10 + 8 = 18

P(blue or green) = 18/40 = 9/20

Therefore, the required probability is 9/20.

3. Answer: C. 3/4

The tokens that are neither yellow nor white are red, blue and green.

Number of favourable tokens = 12 + 10 + 8 = 30

P(neither yellow nor white) = 30/40 = 3/4

The same result can be obtained by subtracting the 10 yellow and white tokens from the total of 40 tokens. Hence, the correct answer is 3/4.

4. Answer: B. 1/130

Initially, there are 4 white tokens among 40 tokens. Therefore, the probability of drawing a white token first is 4/40.

The first token is not replaced. Hence, 3 white tokens remain among 39 total tokens, making the probability of another white token 3/39.

P(both white) = 4/40 × 3/39 = 12/1560 = 1/130

Therefore, the required probability is 1/130.

5. Answer: A. 1/6

The even numbers on the eight-section spinner are 2, 4, 6 and 8.

P(even number on spinner) = 4/8 = 1/2

The numbers greater than 4 on a standard die are 5 and 6, so P(number greater than 4) = 2/6 = 1/3.

The spinner and die are independent. Therefore, P(even number and die result greater than 4) = 1/2 × 1/3 = 1/6.