FDMAT 108 (Mathematical Tools for the Real World)Unit III Exam 2021

Explain whether this makes sense or not and why: “Because there is life on Mars or there is not, the probability of life on Mars is 0.5.”Explain whether this makes sense or not and why: “Based on data showing that we’ve had snow on Christmas in 27 of the past 100 years, the probability of snow this year is 0.27.”Explain whether this makes sense or not and why: The probability of getting heads and tails when you toss a coin is 0, but the probability of getting heads or tails is 1.Explain whether this makes sense or not and why: “I can’t believe you chose the lottery numbers 1-2-3-4-5-6. Getting six numbers in a row is much less likely than getting other random numbers.A covered jar contains 3 green marbles, 5 blue marbles and 9 white marbles and you can’t see these contents. What is the probability that, if you randomized the marbles by shaking the jar and pulled out two marbles in a row (without replacement), you would get 1 blue and 1 green marble pulled in either order?In a mid-season Utah Jazz vs. L.A. Lakers game, suppose Paul Millsap is fouled in a one-and-one situation (meaning he is awarded two free throws only if he makes his first one). Knowing that his season average is 70%, place the following three scenarios in order of highest probability down to the lowest. I) makes both, II) makes first, misses second, III) misses first. (Hint: use a probability tree to help you find the answer.)Explain whether this makes sense or not and why: If you toss a coin four times, it’s much more likely to land in the order HTHT than HHHH. (H stands for heads and T for tails.)