Probability, NAPX-K2-12

Question

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Worked Solution

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Variant 0

DifficultyLevel

438

Question

Eight buttons, numbered 1 to 8, are placed in a bag.

Robin picks three buttons out of the bag without looking.

Once chosen, a button is not put back into the bag.

The first button is number 2.

Which of the following cannot happen?

Worked Solution

Once number 2 is picked, it cannot be picked again (no replacement).

∴\therefore The third button cannot be 2.

Question Type

Multiple Choice (One Answer)

Variables

Variable nameVariable value
question
Eight buttons, numbered 1 to 8, are placed in a bag. Robin picks three buttons out of the bag without looking. Once chosen, a button is not put back into the bag. The first button is number 2. Which of the following cannot happen?
workedSolution
Once number 2 is picked, it cannot be picked again (no replacement). $\therefore$ The third button cannot be 2.
correctAnswer
The third button is 2.

Answers

Is Correct?Answer
x

The second button is even.

✓

The third button is 2.

x

The second button is odd.

x

The third button is 8.

Variant 1

DifficultyLevel

441

Question

Six buttons, numbered 1 to 6, are placed in a bag.

Barney picks four buttons out of the bag without looking.

Once chosen, a button is not put back into the bag.

The first three buttons Barney chose, in order, are 5, 1 and 3.

Which of the following cannot happen?

Worked Solution

Once numbers 5, 3 and 1 are picked, they cannot be picked again (no replacement).

∴\therefore The 4th button chosen cannot be odd →\rightarrow only even numbers left.

Question Type

Multiple Choice (One Answer)

Variables

Variable nameVariable value
question
Six buttons, numbered 1 to 6, are placed in a bag. Barney picks four buttons out of the bag without looking. Once chosen, a button is not put back into the bag. The first three buttons Barney chose, in order, are 5, 1 and 3. Which of the following cannot happen?
workedSolution
Once numbers 5, 3 and 1 are picked, they cannot be picked again (no replacement). $\therefore$ The 4th button chosen cannot be odd $\rightarrow$ only even numbers left.
correctAnswer
The 4th button chosen is odd.

Answers

Is Correct?Answer
x

The 4th button chosen is even.

x

The 4th button chosen is 6.

x

The 4th button chosen is 2.

✓

The 4th button chosen is odd.

Variant 2

DifficultyLevel

439

Question

Seven buttons, numbered 1 to 7, are placed in a bag.

Zac picks four buttons out of the bag without looking.

Once chosen, a button is not put back into the bag.

The first two buttons Zac chose are 6 and 2.

Which of the following cannot happen?

Worked Solution

Once numbers 6 and 2 are picked, they cannot be picked again (no replacement).

∴\therefore The 3rd and 4th picks cannot both be even →\rightarrow only one even number is left.

Question Type

Multiple Choice (One Answer)

Variables

Variable nameVariable value
question
Seven buttons, numbered 1 to 7, are placed in a bag. Zac picks four buttons out of the bag without looking. Once chosen, a button is not put back into the bag. The first two buttons Zac chose are 6 and 2. Which of the following cannot happen?
workedSolution
Once numbers 6 and 2 are picked, they cannot be picked again (no replacement). $\therefore$ The 3rd and 4th picks cannot both be even $\rightarrow$ only one even number is left.
correctAnswer
The 3rd and 4th pick can both be even.

Answers

Is Correct?Answer
x

The 3rd pick can be 4.

✓

The 3rd and 4th pick can both be even.

x

The 4th pick can be 1.

x

The 3rd pick can be odd.

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