Example Question - sample space
Here are examples of questions we've helped users solve.
Calculating Probability of Independent Events
To solve this problem, we need to calculate the probability of two independent events occurring in sequence: 1. Picking a prime number card. 2. Picking a number greater than 4 card. The sample space consists of 8 cards, numbered from 1 to 8. Among these cards, the prime numbers are 2, 3, 5, and 7. Probability of picking a prime number card = number of prime cards / total number of cards P(prime) = 4/8 = 1/2 After picking a prime number, you replace the card and pick again. The number of cards greater than 4 are 5, 6, 7, and 8. Probability of picking a number greater than 4 = number of cards greater than 4 / total number of cards P(greater than 4) = 4/8 = 1/2 Since these are independent events, we can multiply the probabilities: P(prime and greater than 4) = P(prime) * P(greater than 4) P(prime and greater than 4) = (1/2) * (1/2) P(prime and greater than 4) = 1/4 Converting this into a percentage, we get: P(prime and greater than 4) = (1/4) * 100% = 25% Rounded to the nearest tenth of a percent, the answer remains 25.0%.
Understanding Sample Space in Probability
The image contains a handwritten question which is related to probability. The given question is: "A fair coin is tossed and a fair die is thrown together. Find the sample space of the events of a coin." To answer this, firstly, we have to understand the sample space of each individual random experiment. A "fair coin" has two possible outcomes when tossed: Heads (H) or Tails (T). A "fair die" has six possible outcomes when thrown: 1, 2, 3, 4, 5, or 6. However, the question asks only for the sample space of the events of a coin, which means we are only interested in the outcomes of the coin toss, regardless of the die result. The sample space for the coin alone is simply: S_coin = {H, T} If we were to find the combined sample space of tossing a coin and throwing a die together, we would list all possible pairs of outcomes, one from the coin and one from the die. But since the question only asks for the sample space of the coin, the answer provided is sufficient.
Sample Space and Outcomes in Coin Tossing Experiment
The question appears to be related to probability and asks for the description of the sample space and outcomes for a trial in which 2 coins are tossed, and each coin can show either a head (H) or a tail (T). The sample space for this experiment (tossing two coins) consists of all the possible outcomes that can occur. Since each coin has 2 possible outcomes, and there are 2 coins, there are 2 x 2 = 4 possible outcomes in total for the sample space \( S \). The sample space can be written as: \[ S = \{ (H, H), (H, T), (T, H), (T, T) \} \] Here, each pair represents the outcome of the two coins, with the first element in the pair representing the outcome of the first coin, and the second element representing the outcome of the second coin.
CamTutor
In regards to math, we are professionals.
Get In Touch
Email: camtutor.ai@gmail.com