PSAT Math : How to find the probability of an outcome

Study concepts, example questions & explanations for PSAT Math

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Example Questions

Example Question #58 : Probability

A bag contains the following numbers of apples:  12 red delicious, 10 granny smith, and 7 fuji apples.  If an apple is selected at random, what is the probability it is either a granny smith or a fuji apple?

Possible Answers:

Correct answer:

Explanation:

Probability = desired outcomes divided by total possible outcomes. Desired outcome can be either fuji or granny smith.

Desired outcomes

Total outcomes

Example Question #59 : Probability

From a class consisting of 15 girls and 12 boys, two students are chosen at random to be class representatives.  What is the probability that neither of the two students chosen is a boy?

Possible Answers:

Correct answer:

Explanation:

To satisfy the question, BOTH students chosen must be girls.  

First selection: 15 girls of 27 total students:

Second selection: 14 girls out of 26 total students:

Example Question #60 : Probability

If 2 six-sided dice, each with sides numbered 1-6, are rolled, what is the probability that the sum of the numbers on the face-up sides is equal to 7?

Possible Answers:

Correct answer:

Explanation:

Probability = desired outcomes divided by total possible outcomes. 

Desired outcomes = 6   (1,6; 2,5; 3,4; 4,3; 5,2; 6;1)

Total outcomes - 36 

Example Question #61 : How To Find The Probability Of An Outcome

If an 8-sided die is rolled 3 times, what is the probability that the same number will be rolled each time?

Possible Answers:

Correct answer:

Explanation:

Another way to look a it is there are 512 total possible outcomes  and 8 desired outcomes.

Example Question #62 : How To Find The Probability Of An Outcome

If a two-sided coin is flipped four times, what is the probability of never getting a head?

Possible Answers:

\frac{1}{2}

\frac{3}{8}

\frac{1}{16}

\frac{5}{16}

\frac{7}{16}

Correct answer:

\frac{1}{16}

Explanation:

The probability of never getting a head is the same as always getting tails. This is \frac{1}{2}\times \frac{1}{2}\times \frac{1}{2}\times \frac{1}{2}=\frac{1}{16}.

Example Question #63 : How To Find The Probability Of An Outcome

If a six-sided die is thrown four times, what is the probability of getting a four everytime?

Possible Answers:

\frac{1}{1296}

\frac{1}{7776}

\frac{1}{2}

\frac{1}{216}

\frac{1}{50}

Correct answer:

\frac{1}{1296}

Explanation:

The probability is \frac{1}{6}\times \frac{1}{6}\times \frac{1}{6}\times \frac{1}{6}=\frac{1}{1296}.

Example Question #64 : How To Find The Probability Of An Outcome

If there are 9 marbles in a bag, three white, three blue, and three red, what is the probability of selecting three red marbles at random?

Possible Answers:

Correct answer:

Explanation:

The probability of selecting 3 red marbles is .

Example Question #65 : How To Find The Probability Of An Outcome

There is a box containing 2 red marbles, 7 blue marbles, and an unknown number of green marbles. If the probably of drawing a red marble is 10%, what is the probably that one draws a green marble? 

Possible Answers:

70\%

55\%

60\%

50\%

20\%

Correct answer:

55\%

Explanation:

Let x be the total number of marbles in the box. Since there's a 10% chance of drawing a red marble, then 0.1x=2 implies there are 20 marbles total in the box. Thus, there are only 11 green marbles, resulting in the probability of drawing a green marble being \frac{11}{20}=55\%

Example Question #66 : How To Find The Probability Of An Outcome

A person rolls a fair 6-sided die twice. What is the probability that the sum of the two rolls is 3?

Possible Answers:

\frac{1}{18}

\frac{2}{9}

\frac{1}{9}

\frac{1}{3}

\frac{1}{36}

Correct answer:

\frac{1}{18}

Explanation:

In order for the sum to be 3, the two rolls must be 1 and 2. However, it doesn't matter which one comes first. Therefore, there are 2 ways we can acquire the sum being 3. The total number of combination of two die is 6\cdot 6=36.

Thus, the probability of rolling a sum of 3 is \frac{2}{36}=\frac{1}{18}.

Example Question #67 : How To Find The Probability Of An Outcome

A card is drawn randomly from a stardard 52-card deck. What is the probability of drawing a four of hearts?

Possible Answers:

\frac{1}{13}

\frac{1}{52}

\frac{3}{52}

\frac{1}{4}

\frac{2}{13}

Correct answer:

\frac{1}{52}

Explanation:

The question is asking for the probability of drawing a 4 AND a Heart.

Prob(draw a 4) =\frac{4}{52}=\frac{1}{13}.

Prob(draw a Heart) =\frac{13}{52}=\frac{1}{4}.

Then the Prob(4 AND Heart) = Prob(4) * Prob(Heart) =\frac{1}{13}\cdot \frac{1}{4}=\frac{1}{52}

You can also solve this question using logic instead of the rules of probability. We know there is only one four of hearts in a deck of cards, so the probability of drawing one must be \frac{1}{52}.

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