smc-675-10-Core concepts

Probability, NAP-K3-CA02

There are 20 raffle tickets, numbered 1 to 20, in a box.

Three prizes are given away by choosing three tickets from the box. One ticket can win one prize only.

The first ticket drawn is number 15 and wins the third prize.

Which of the following is not possible?

	Second prize is won by number 2.
	First prize is won by a prime number.
	Second prize is an even number.
	First prize is won by number 15.

Show Answers Only

`text(First prize is won by number 15.)`

Show Worked Solution

`text(First prize is won by number 15 is impossible because)`

`text(number 15 has already been chosen and won 3rd prize.)`

`text{(Note that there is no replacement of tickets.)}`

Probability, NAP-A3-NC08

Ryan has white and black marbles in his bag.

If he chooses one without looking he is likely, but not certain, to get a white marble.

Which is Ryan's bag?

Show Answers Only

Show Worked Solution

`text(The 1st option gives a)\ \ 3/5\ \ text(chance for a)`

`text{white marble (likely but not certain).}`

Probability, NAP-J3-CA19

Mick has a bag of marbles. His marbles are orange, white, blue and green.

Mick picks one marble from his bag.

Which of the following could be the probability that the marble he picks is green.

`13/3`	`1.52`	`3/13`	`6`

Show Answers Only

`3/13`

Show Worked Solution

`text(Any probability must be between 0 and 1.)`

`:.\ text(Only possibility is)\ 3/13`

Probability, NAP-E3-CA17

Peter has a bag of marbles. 75% of his marbles are blue.

Peter takes a green marble from his bag and loses it in a game.

If he takes another marble from the bag without looking, what are the chances it is blue?

	less than 75%
	equal to 75%
	greater than 75%

Show Answers Only

`text(greater than 75%)`

Show Worked Solution

`text(There will be greater than 75% chance)`

`text(because there are the same amount of )`

`text(blue marbles to be chosen but 1 less)`

`text(in the bag.)`

Probability, NAP-F3-CA13

Which spinner does not show a 50-50 chance of landing on the `Delta` symbol?

Show Answers Only

Show Worked Solution

`text(Each section that has a triangle in it in the above image)`

`text(only accounts for)\ \ 1/6\ \ text(of the pie.)`

`:.\ text(The spinner only has)\ \ 1/3\ \ text(chance of landing)`

`text(on a triangle.)`

Probability, NAP-E3-NC06

Jack rolls a standard dice three times.

He rolls a six each time.

Jack then has a forth roll.

Which of the following is true?

	He is more likely to roll a six than a four.
	He is certain to roll a six.
	He has an equal chance of rolling a six as a four.
	He is more likely to roll a four then a six.

Show Answers Only

`text(He has an equal chance of rolling a six as a four.)`

Show Worked Solution

`text(S)text(ince all numbers have an equal chance)`

`text(of being rolled,)`

`=>\ text(He has an equal chance of rolling a six as a four.)`

Probability, NAP-I3-NC06 SA

Peter has a marble bag that contains 20 marbles that are either red or green in colour.

The probability of randomly picking a green marble is 70%.

What is the probability of randomly picking a red marble?

Show Answers Only

`text(30%)`

Show Worked Solution

`P(text(green)) + P(text(red))`	`= 100text(%)`
`text(70%)\ + P(text(red))`	`= 100text(%)`
`:. P(text(red))`	`= 30text(%)`