SSAT Middle Level Math : How to find the probability of an outcome

Study concepts, example questions & explanations for SSAT Middle Level Math

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Example Questions

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Example Question #1 : How To Find The Probability Of An Outcome

A pair of fair dice are rolled. What is the probability that the sum will be a multiple of 3?

Possible Answers:

Correct answer:

Explanation:

There are four possible multiples of 3 that can come out: 3,6,9, and 12. There are 36 equally probable outcomes; the following will result in a multiple of 3:

These are 12 outcomes out of 36, making the probability 

Example Question #1 : How To Find The Probability Of An Outcome

A pair of fair dice are rolled. What is the probability that the sum will be a multiple of 4?

Possible Answers:

Correct answer:

Explanation:

There are three possible multiples of 4 that can come out: 4, 8, and 12. There are 36 equally probable outcomes; the following will result in a multiple of 4:

These are 9 outcomes out of 36, making the probability 

Example Question #2 : How To Find The Probability Of An Outcome

Some balls are placed in a hat - ten red, four blue, six yellow. What is the probability that a randomly drawn ball will not be blue?

Possible Answers:

Correct answer:

Explanation:

There are 20 balls in the hat. All but four - that is, sixteen - are blue, so the probability of a draw resulting in a non-blue ball is 

Example Question #3 : Outcomes

The red jacks are removed from a standard deck of fifty-two cards. What is the probability that a card randomly drawn from that modified deck will be black?

Possible Answers:

Correct answer:

Explanation:

The removal of two red jacks - and no black cards - results in there being fifty cards, twenty-six of them black. Therefore, the probability of a randomly drawn card being black is .

Example Question #4 : How To Find The Probability Of An Outcome

A standard deck of cards is modified by adding the red threes from another deck. What is the probability that a card randomly drawn from that modified deck will be a red card?

Possible Answers:

Correct answer:

Explanation:

The addition of two red threes from another deck results in the deck comprising fifty-four cards, twenty-eight of which are red. Therefore, the probability of a randomly drawn card being red is 

Example Question #5 : How To Find The Probability Of An Outcome

A standard deck of cards is modified by adding the red queens from another deck. What is the probability that a card randomly drawn from that modified deck will be a face card (jack, queen, king)?

Possible Answers:

Correct answer:

Explanation:

There are four cards of each rank in a standard deck; since three ranks - jacks, queens, kings - are considered face cards, this makes twelve face cards out of the fifty-two. But two more face cards - two red queens - have been introduced, so now there are fourteen face cards out of fifty-four. This makes the probability of a randomly drawn card being a face card

Example Question #3 : How To Find The Probability Of An Outcome

In a bag of marbles, there are  blue marbles,  red marbles, and  green marbles. What is the probability of drawing two blue marbles in a row?

Possible Answers:

3

Correct answer:

Explanation:

The probability of drawing a blue marble on the first try is , since there are  blue marbles out of a total of  marbles. The probability of drawing a second blue marble is , since now there are  blue marbles remaining out of a total of  remaining marbles. The probability of drawing two blue marbles in a row is the product of the individual probabilities: .

Example Question #4 : How To Find The Probability Of An Outcome

Dave has a sock drawer with 8 blue and 10 black socks. 

If Dave pulls out one black sock, what is the probability that the next sock he pulls out of the drawer is also black?

Possible Answers:

4 out of 9

10 out of 17

1 out of 2

5 out of 9

9 out of 17

Correct answer:

9 out of 17

Explanation:

Since the first sock that Dave pulls out is black, there are 17 remaining socks in the drawer, 8 blue and 9 black. The probability that Dave will choose another black is sock is therefore 9 out of 17.

Example Question #8 : How To Find The Probability Of An Outcome

If Mark flips a coin and then rolls a die, what are the odds that the coin will be heads and that the die will land on a multiple of 3?

Possible Answers:

Correct answer:

Explanation:

If Mark flips a coin, the chance that it will land on heads is . On a die, there are 2 out of 6 numbers that are a multiple of 3 (3 and 6); therefore, there is a  chance that the dice will be a multiple of 3. 

The probability that the coin will land on heads and that the dice will be a multiple of 3 is:

Example Question #6 : How To Find The Probability Of An Outcome

Lisa and Fred were flipping a quarter and recording whether it was heads or tails. What is the probability they flip a quarter and it lands on heads, heads, tails, heads, tails? (H,H,T,H,T)

Possible Answers:

Correct answer:

Explanation:

There are two possibilities every time you flip a coin and only one outcome. Therefore the probability for flipping either heads or tails each time is . When you have multiple trials in a row you multiply the probabilities of each outcome by each other. 

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