Sample Space and Probability Quiz

What is the sample space when a single six-sided die is rolled?

Answer explanation

The sample space for rolling a single six-sided die includes all possible outcomes. Since the die has faces numbered from 1 to 6, the correct sample space is {1, 2, 3, 4, 5, 6}.

Define the sample space for flipping a coin.

Answer explanation

The sample space for flipping a coin includes all possible outcomes. The correct choice, \{Heads, Tails\}, represents the two outcomes when a coin is flipped. The other options are incomplete or incorrect.

If a coin is flipped twice, what is the sample space?

Answer explanation

The sample space for flipping a coin twice includes all possible outcomes: HH (heads, heads), HT (heads, tails), TH (tails, heads), and TT (tails, tails). Thus, the correct answer is \{HH, HT, TH, TT\}.

What is the probability of rolling a 4 on a six-sided die?

Answer explanation

A six-sided die has 6 faces, each showing a different number from 1 to 6. The probability of rolling any specific number, including a 4, is the number of favorable outcomes (1) divided by the total outcomes (6), which is \(\frac{1}{6}\).

If a die is rolled 60 times and the number 3 appears 15 times, what is the experimental probability of rolling a 3?

Answer explanation

The experimental probability of rolling a 3 is calculated by dividing the number of times 3 appears (15) by the total rolls (60). Thus, \( \frac{15}{60} = \frac{1}{4} \). Therefore, the correct answer is \( \frac{1}{4} \).

What is the sample space for drawing a card from a standard deck of 52 cards?

Answer explanation

The sample space for drawing a card from a standard deck includes all individual cards. The correct choice lists all 52 cards, represented as {2♥, 3♥, ..., A♠}, which encompasses every card in the deck.

If a spinner is divided into 4 equal sections labeled A, B, C, and D, what is the sample space?

Answer explanation

The sample space represents all possible outcomes of the spinner. Since it has 4 equal sections labeled A, B, C, and D, the correct sample space is {A, B, C, D}. Other options include extra labels that do not exist.

If a coin is flipped 100 times and lands on heads 55 times, what is the experimental probability of getting heads?

Answer explanation

The experimental probability of getting heads is calculated by dividing the number of heads (55) by the total flips (100). Thus, 55/100 = 0.55, making the correct answer 0.55.

What is the probability of drawing a heart from a standard deck of 52 cards?

Answer explanation

A standard deck has 52 cards, with 13 hearts. The probability of drawing a heart is the number of hearts divided by the total number of cards: \( \frac{13}{52} = \frac{1}{4} \). Thus, the correct answer is \( \frac{1}{4} \).

If a six-sided die is rolled 30 times and the number 5 appears 6 times, what is the experimental probability of rolling a 5?

Answer explanation

The experimental probability of rolling a 5 is calculated by dividing the number of times 5 appeared (6) by the total rolls (30). Thus, \( \frac{6}{30} = \frac{1}{5} \). Therefore, the correct answer is \( \frac{1}{5} \).