Your initial post should be 75-150 words in length.Conditional Probability1. If there are 3 green marbles and 4 red marbles in a bag, and you were asked to draw one without looking, what is the probability of drawing one green marble? Please show work 2. If you don't put that marble back, what is the probability of drawing another green marble? Please show work 3. Using the above "marbles in the bag" scenario, what is a conditional probability question that you can make from it? In §4.4 we are introduced to the concept of conditional probability. The notation P(A | B) denotes the probability of event A occurring given that we know event B has occurred.Now consider the Monty Hall Problem introduced in the following video: https://m.youtube.com/watch?v=4Lb-6rxZxx0 4. After watching this video, we know that if we are given the option to switch doors that, probabilistically speaking, it is in our best interest to switch. Why is the probability of winning NOT 50/50 when the contestant is given the opportunity to switch?Please provide original work. No plagiarizing.

Attached is the prompt along with the rubric and template and supporting documents needed

Topic 1: Confidence Interval View Full Description Confidence Intervals for the Mean sigma knownMain PostAssuming .05 as your alpha value, make up a problem similar to this one. Make up 36 gas prices for your example. Use price values in your list that some you made up and be sure they are similar to the prices you have had in your area. List the values in your post.Instructions for your response. You will respond to at least 2 classmates.In your response, describe what you did and give the mean, standard deviation and confidence interval.Example below: First find the mean. List all 36 gas prices in cells A1 to A36 in your excel spreadsheet. On a different cell type in =average(A1:A36) and the hit enter to find the average Assume your answer is 2.65 On a different cell type in =stdev.s(A1:A36) or =stdevA(A1:A36) and enter to find the standard deviation Assume your answer is .43 Then type this in an excel cell =confidence(.05,.43,36) and hit enter. This is the E value So take the mean of 2.65 and you have (2.65-E, 2.65+E) for your confidence interval Formula you used above for the confidence interval:The formula is E= zsubc * sigma / sqrt nWhere the left hand endpoint is xbar - E and the right hand endpoint is xbar + EJust a review of your instructions: First you will make up a problem with alpha = .05 and give the values for the problem. This is your main post. Then will make 2 responses explaining all work and giving the solutions to 2 classmates problems. Instructions: Your initial post should be at least 250 words. Please respond to at least 2 other students. Responses should be a minimum of 100 words and include direct questions.To earn full credit for this forum, you must respond to at least two (2) of your peers and post your initial post by Thurs.