Unit 8 Review: Probability (Basic Algebra 2)

Two coins are tossed. What is the probability that both will land on heads?

Answer explanation

When tossing two coins, each coin has 2 outcomes: heads (H) or tails (T). The total outcomes are HH, HT, TH, TT, making 4 possible combinations. Only 1 combination (HH) results in both coins landing on heads. Thus, the probability is \frac{1}{4}.

A bag contains 5 red balls and 3 blue balls (total of 8). If two balls are drawn at random without replacement, what is the probability that both are red?

Answer explanation

To find the probability of drawing 2 red balls without replacement, calculate: P(Red 1) = 5/8, then P(Red 2 | Red 1) = 4/7. Thus, P(both red) = (5/8) * (4/7) = 20/56 = 5/14. The correct answer is \frac{5}{14}.

A die is rolled. What is the theoretical probability of getting a number greater than 4?

Answer explanation

A die has 6 faces numbered 1 to 6. The numbers greater than 4 are 5 and 6, which are 2 outcomes. The total outcomes are 6. Thus, the probability is \( \frac{2}{6} = \frac{1}{3} \).

Given the following two-way table for students' favorite subjects: What is the probability that a randomly selected student is a girl who prefers Science?

Answer explanation

To find the probability of selecting a girl who prefers Science, divide the number of girls who prefer Science by the total number of students. If there are 2 girls who prefer Science out of 20 students, the probability is \frac{2}{20} = \frac{1}{10}.

Answer explanation

To find P(A and B), use the formula P(A|B) * P(B). Here, P(A|B) = 7/10 and P(B) = 1/2. Thus, P(A and B) = (7/10) * (1/2) = 7/20. Therefore, the correct answer is \frac{7}{20}.

A spinner is spun 100 times and lands on red 28 times. What is the experimental probability of landing on red?

Answer explanation

The experimental probability of landing on red is calculated by dividing the number of times red was landed on (28) by the total spins (100). Thus, the probability is \(\frac{28}{100}\), which is the correct answer.

Answer explanation

To find P(A|B), use the formula P(A|B) = P(A and B) / P(B). Here, P(A and B) = 1/5 and P(B) = 1/2. Thus, P(A|B) = (1/5) / (1/2) = (1/5) * (2/1) = 2/5. The correct answer is \frac{2}{5}.

A box contains 4 white and 6 black balls (10 Total). Two balls are drawn at random with replacement. What is the probability that both are black?

Answer explanation

The probability of drawing a black ball is \frac{6}{10} = \frac{3}{5}. Since the draws are with replacement, the probability of both being black is \left(\frac{3}{5}\right) \times \left(\frac{3}{5}\right) = \frac{9}{25}. However, \frac{36}{100} is equivalent to \frac{9}{25}, making it the correct choice.

Given the following two-way table for survey responses: What is the probability that a randomly selected respondent is female or answered "No"?

Answer explanation

To find the probability of selecting a female or a 'No' response, use the formula P(A or B) = P(A) + P(B) - P(A and B). Here, P(female) = 3/5 and P(No) = 2/5, with P(female and No) = 0. Thus, P(female or No) = 3/5 + 2/5 - 0 = 3/5.

A coin is tossed 50 times and lands on heads 28 times. What is the experimental probability of getting tails?

Answer explanation

The coin was tossed 50 times, landing on heads 28 times. Therefore, tails occurred 50 - 28 = 22 times. The experimental probability of getting tails is \( \frac{22}{50} \). Thus, the correct answer is \( \frac{22}{50} \).