Nicholas performs an experiment in which he pulls a marble from a bag. In his experiment, he finds that he is twice as likely to pull a red marble as a blue marble. If Nicholas pulls 10 red marbles, how many blue marbles does he pull?

A bag of jellybeans has 20 watermelon jellybeans, 45 sour apple jellybeans, 30 orange jellybeans and 5 cotton candy jellybeans. If you reach in and grab one jelly bean, what is the probability that it will be watermelon flavored?

Possible Answers:

4/19

1/4

1/20

1/3

1/5

Correct

1/5

Explanation:

Add up the total number of jellybeans, 20 + 45 + 30 + 5 = 100.

Divide the number of watermelon jellybeans by the total: 20/100 and reduce the fraction to 1/5.

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Find The Probability Of An Outcome : Example Question #2

A circle is inscribed inside a square. If a point inside the square is selected at random, what is the probability that the point will also be inside the circle?

Possible Answers:

5/6

π/6

3/4

π/4

Correct

π/4

Explanation:

The probability of the point being inside the circle is the ratio of the area of the circle to the area of the square. If we suppose that the circle has radius r, then the square must have side 2r. The area of the circle is πr2 and the area of the square is 〖(2r)〗2=〖4r〗2, so the proportion of the areas is (πr2)/〖4r〗2 =π/4.

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Find The Probability Of An Outcome : Example Question #3

John has a bowl with 54 marbles in it. Half of the marbles are green and half of the marbles are blue. John takes 3 green marbles and 6 blue marbles from the jar. John then takes 13 additional marbles from the remaining marbles in the jar. What is the minimum number of these 13 marbles that must be green in order for there to be more blue marbles than green marbles left?

Possible Answers:

8

5

4

9

10

Correct

9

Explanation:

The bowl has 54 marbles, half green and half blue. This gives us 27 green and 27 blue marbles:

27 G / 27 B

John then takes 3 green and 6 blue from the bowl. This leaves the bowl with:

24 G / 21 B

If there are going to be more blue than green marbles after John's 13 marbles, he has to take at least 4 more green marbles than blue marbles, because right now there are 3 less blue marbles. Therefore, we need to take at least 9 green marbles, which would mean 4 or less of the marbles would be blue (8 green and 5 blue would leave us with equal green and equal blue marbles, so it would have to be more than 8 green marbles, which gives us 9 green marbles).

We can also solve this as an inequality. You take the difference in marbles, which is 3, which means you need the difference in green and blue marbles to be greater than 3, or at least 4. You have b + g = 13 and g - b > 3, where b and g are positive integers.

b + g = 13 (Subtract g on both sides of the equation)

b = 13 - g

g - b > 3 (Substitute above equation)

g - (13 - g) > 3 (Distribute negative sign in parentheses)

g - 13 + g > 3 (Add both g variables)

2g - 13 > 3 (Add 13 to both sides of the inequality)

2g > 16 (Divide both sides of the inequality by 2)

g > 8 so g has to be 9 or greater.

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Find The Probability Of An Outcome : Example Question #4

If x is chosen at random from the set (4, 6, 7, 9, 11) and y is chosen at random from the set (12, 13, 15, 17) then what is the probability that xy is odd?

Possible Answers:

3/10

11/20

9/10

6/10

9/20

Correct

9/20

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step-by-step explanation:

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