Probability Test Practice

A fair 17-sided die is shown. How many outcomes are in the sample space when rolling the die two times?

• 2

• 17

• 34

• 289

Answer explanation

When rolling a die twice, each roll has 17 possible outcomes. Therefore, the total outcomes are 17 (first roll) x 17 (second roll) = 289.

What is the theoretical probability of choosing two red marbles in a row?

• 1/6

• 2/6

• 1/36

• 2/36

Answer explanation

To find the probability of choosing two red marbles in a row, multiply the probability of choosing a red marble first (1/6) by the probability of choosing a red marble second (1/6). Thus, 1/6 * 1/6 = 1/36.

A fair 17 sided die is shown. Determine the theoretical probability of rolling a number that is divisible by 3 two times in a row.

Type your answer as a decimal rounded to the nearest thousandth.

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Answer explanation

The numbers divisible by 3 on a 17 sided die are 3, 6, 9, 12, and 15. Therefore on the first roll there is a 5/ 17 chance and on the second roll there is a 5/17 chance. The probability of rolling one of these numbers on both roll is (5/17)x(5/17) or 25/289. As a percent rounded to the nearest tenth that is 8.7%.

Each letter of the work MISSISSIPPI is written on a card and put into a bag. What is the theoretical probability of choosing an "I", putting it back and then drawing a "P"?

• 6.6%

• 1.7%

• 2.5%

• 6.7%

Answer explanation

The word 'MISSISSIPPI' has 11 letters: 4 I's and 2 P's. The probability of drawing an I is 4/11, and for P is 2/11. Thus, the combined probability is (4/11) * (2/11) = 2/121 which is equal to 0.0661157025, which is approximately 6.6%.

Determine the experimental probability of P(R, A). Type your answer as a percentage rounded to the nearest tenth.

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Answer explanation

To find the experimental P(R, A), divide the number of times (R,A) occurred (7) by the total number trials (64). Multiply by 100 to convert to a percentage, then round to the nearest tenth for the final answer.

If Elizabeth conducted a second experiment and spun the spinner twice 700 times, she would expect the new results to ...

• have exactly the same experimental probabilities as in the first experiment.

• have experimental probabilities that are closer to the theoretical probabilities than the first experiment.

• have outcomes that are exactly 10 times the outcomes of the first experiment.

• have experimental probabilities that are exactly twice as much as in the first experiment.

Answer explanation

In a larger sample size of 1400 spins, the experimental probabilities are likely to converge closer to the theoretical probabilities due to the law of large numbers, making this the correct choice.

If you roll a regular six-sided die 240 times, how many times should you expect to roll a 5?

• 40

• 80

• 120

• 200

Answer explanation

When rolling a six-sided die, the probability of rolling a 5 is 1/6. Therefore, in 240 rolls, you expect to roll a 5 about 240 * (1/6) = 40 times. Thus, the correct answer is 40.

A bag has 3 red marbles, 2 blue and 4 yellow. What is the theoretical probability of pulling a red?

• 3/10

• 3/9

• 1/9

• 1/3

Answer explanation

To find the probability of pulling a red marble, divide the number of red marbles (3) by the total number of marbles (3 + 2 + 4 = 9). Thus, the probability is 3/9, which simplifies to 1/3.

Tags

CCSS.5.NF.B.3

Which of these correctly represents the sample space of flipping a regular coin 3 times, where H represents heads and T represents tails?

• {1/2, 1/2, 1/2}

• {H or T, H or T, H or T}

• {HHH, HTH, HTT, THH, THT, TTT}

• {HHH, HHT, HTH, HTT, THH, THT, TTH, TTT}

Answer explanation

The correct sample space for flipping a coin 3 times includes all possible outcomes: HHH, HHT, HTH, HTT, THH, THT, TTH, and TTT. This is represented by the choice {HHH, HHT, HTH, HTT, THH, THT, TTH, TTT}.