Example Question - probability problem
Here are examples of questions we've helped users solve.
Probability Problem Involving Spinner
I can see that the image contains a question about a probability problem involving a spinner. The problem states that the spinner is divided into equally sized sections, 3 of which are gray and 5 of which are blue. The question asks for the probability that the first spin lands on gray and the second spin lands on blue. To solve this, we need to calculate the probability of both events happening one after the other. The chance that the first spin lands on gray is 3 out of 8, as there are 3 gray sections out of a total of 8. The probability of a specific event is calculated by the formula: \[ P(\text{Event}) = \frac{\text{number of favorable outcomes}}{\text{total number of possible outcomes}} \] For the first spin: \[ P(\text{first spin on gray}) = \frac{3}{8} \] For the second spin, the probability that the spin lands on blue is 5 out of 8, as there are 5 blue sections. For the second spin: \[ P(\text{second spin on blue}) = \frac{5}{8} \] Since these are independent events, the overall probability of both occurring in sequence is the product of the two individual probabilities: \[ P(\text{gray then blue}) = P(\text{first spin on gray}) \times P(\text{second spin on blue}) \] \[ P(\text{gray then blue}) = \left( \frac{3}{8} \right) \times \left( \frac{5}{8} \right) \] \[ P(\text{gray then blue}) = \frac{3 \times 5}{8 \times 8} \] \[ P(\text{gray then blue}) = \frac{15}{64} \] So, the probability that the first spin lands on gray and the second spin lands on blue is \(\frac{15}{64}\).
Solving Probability Problem with Partial Information
The image shows a statistics problem which is partially obscured and difficult to read. However, I will piece together what is visible and attempt to solve it. The problem states that there are 18 Democrats (half Democrats, half Republicans), and 32 representatives (half Democrats, half Republicans) who wish to serve on a joint congressional committee on tax reform. A five-person committee is chosen at random. Based on what I can see: - There are 36 Democrats in total (half of 18 Senators and half of 32 Representatives). - There are 36 Republicans in total (other halves of Senators and Representatives). For part A, the first question seems to be about the probability that the committee contains an equal number of Senators and Representatives. However, since the specific number of Senators and Representatives required is not visible, it's impossible to calculate the probability accurately without further information. For part B, the probability that the committee contains equal numbers of Republicans and Democrats is asked for. Since there are an odd number of people on the committee (5), it's impossible to have an equal number of Republicans and Democrats. So the probability for part B would be 0. To provide an accurate and complete answer, the full details of the question would be needed. Could you please provide the full text of the problem?
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