SAT Math : How to find the probability of an outcome

Study concepts, example questions & explanations for SAT Math

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Example Questions

Example Question #61 : Probability

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

Possible Answers:

\frac{1}{2}

\frac{7}{16}

\frac{1}{16}

\frac{5}{16}

\frac{3}{8}

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 #62 : Probability

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

Possible Answers:

\frac{1}{7776}

\frac{1}{216}

\frac{1}{2}

\frac{1}{50}

\frac{1}{1296}

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 #63 : Probability

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 #64 : Probability

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:

55\%

50\%

20\%

60\%

70\%

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 #65 : Probability

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{2}{9}

\frac{1}{18}

\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 #66 : Probability

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

Possible Answers:

\frac{3}{52}

\frac{1}{13}

\frac{2}{13}

\frac{1}{4}

\frac{1}{52}

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}.

Example Question #67 : Probability

How many different ways can 15 runners receive ribbons in a race if 1st, 2nd, 3rd, and 4th place ribbons are given?

Possible Answers:

_{4}P_{15}

_{15}C_{4}

_{15}P_{4}

_{4}C_{15}

15!

Correct answer:

_{15}P_{4}

Explanation:

Order matters, so a permutation of 15 things chosen 4 at a time, or _{15}P_{4}, is the correct answer.

Example Question #231 : Data Analysis

A bag of marbles consists of 13 green, 15 blue, 12 black and an unknown number of red marbles. If the chance of choosing a red marble is 1 in 3, how many marbles are there total?

Possible Answers:

60

40

56

45

54

Correct answer:

60

Explanation:

Adding the green, blue, and black marbles together gives 40. Then if there is a \frac{1}{3} chance that a red marble is drawn, there must be an additional 20 marbles.

Example Question #232 : Data Analysis

Tiffany picks a peice of fruit from a bowl at random.  The bowl contains 2 red delicious apples, 3 granny smith apples, 1 orange and 3 grapefruits.  What is the probability that she chooses an apple?

Possible Answers:

Correct answer:

Explanation:

The chance she picks an apple is the total number of apples over the total number of fruits in the bowl.  Since there are 2 kinds of apples, we add 2 red delicious and 3 granny smiths to get 5 apples total.  In addition there are 4 more peices of fruit, so the total number of fruits is 9.

Example Question #233 : Data Analysis

In a bag, there are 6 black marbles and 8 yellow marbles. What is the possibility of choosing a yellow marble at random?

Possible Answers:

\dpi{100} \small \frac{3}{4}

\dpi{100} \small \frac{4}{3}

\dpi{100} \small \frac{3}{7}

\dpi{100} \small \frac{4}{7}

Correct answer:

\dpi{100} \small \frac{4}{7}

Explanation:

There is a total of 14 marbles, of which, 8 are yellow; therefore the probability of choosing a yellow marble is \dpi{100} \small \frac{8}{14} or \dpi{100} \small \frac{4}{7}

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