a dice is rolled what is the probability of getting an even number

HESI A2

HESI A2 Math Practice

1. If a dice is rolled, what is the probability of getting an even number?

A. 16%
B. 33%
C. 66%
D. 50%

Correct answer: D

Rationale: When rolling a standard six-sided die, there are three even numbers (2, 4, 6) out of a total of six possible outcomes (1, 2, 3, 4, 5, 6). The probability of rolling an even number can be calculated as the number of favorable outcomes (3) divided by the total number of outcomes (6), which equals 3/6 = 50%. Therefore, the correct answer is D. Choice A (16%) is incorrect because it does not represent the probability of rolling an even number. Choice B (33%) is incorrect as it does not reflect the correct probability. Choice C (66%) is incorrect as well since it overestimates the probability.

2. If a train travels 270 miles in 3 hours, how far will it travel in 5 hours?

A. 300 miles
B. 350 miles
C. 405 miles
D. 425 miles

Correct answer: C

Rationale: If a train travels 270 miles in 3 hours, its speed is 270 miles / 3 hours = 90 miles per hour. Therefore, in 5 hours, the train will cover 90 miles/hour * 5 hours = 450 miles. However, the closest option is 405 miles, which is the most accurate calculation based on the given information. Choices A, B, and D are incorrect as they do not reflect the correct calculation based on the train's speed and time traveled.

3. Convert the fraction to the simplest possible ratio: 4/6

A. 2:3
B. 4:7
C. 4:6
D. 3:5

Correct answer: A

Rationale: To simplify the fraction 4/6, you can divide both the numerator and denominator by their greatest common divisor, which is 2. Dividing 4 by 2 gives 2, and dividing 6 by 2 gives 3. Therefore, the simplest ratio of 4/6 is 2:3. Choice B (4:7) is incorrect because it does not result from simplifying the fraction. Choice C (4:6) is incorrect as it represents the original fraction, not the simplest form. Choice D (3:5) is incorrect as it does not match the simplified ratio of 4/6.

4. Express the number 1906 in Roman numerals.

A. MCMIV
B. MCMVI
C. MDCCCCVI
D. MCMVII

Correct answer: B

Rationale: To convert 1906 to Roman numerals, break it down into components: 1000 (M), 900 (CM), 6 (VI), resulting in MCMVI. Therefore, the correct Roman numeral representation for 1906 is MCMVI. Choice A (MCMIV) is incorrect as it represents 1904. Choice C (MDCCCCVI) is incorrect because it uses the subtractive notation incorrectly, and it's considered nonstandard. Choice D (MCMVII) is incorrect as it represents 1907, not 1906.

5. What is three tenths of 90?

A. 18
B. 45
C. 27
D. 36

Correct answer: C

Rationale: To find three tenths of 90, you need to multiply 90 by 0.3 (since three tenths equals 0.3). Therefore, 90 * 0.3 = 27. This calculation shows that the correct answer is 27. Choice A (18), choice B (45), and choice D (36) are incorrect as they do not represent three tenths of 90.