Use the images and solve from a - f correctly please d. Use the special addition rule and the probability distribution to determine the probability that the year had at least one major hurricane. e. Use the special addition rule and the probability distribution to determine the probability that the year had exactly eight major hurricanes. f. Use the special addition rule and the probability distribution to determine the probability that the year had between 6 and 8 major hurricanes, inclusive a. Use random-variable notation to represent the event that the year had at least one major hurricane. Select the correct choice below and fill in the answer box within your choice.O A. {Y21}B. P()b. Use random-variable notation to represent the event that the year had exactly eight major hurricanes. Select the correct choice below and fill in the answer box within your choice.KA. P()B. {Y=8}c. Use random-variable notation to represent the event that the year had between 6 and 8 major hurricanes, inclusive. Select the correct choice below and fill in the answer box within your choice.O A. (6sY<8'}O B. P() A certain hurricane database extends back to 1851, recording among other data the number of major hurricanes (measuring at least a Category 3) striking a certain regionper year. The following table provides a probability distribution for the number of major hurricanes, Y, for a randomly selected year between 1851 and 2012. Completeparts (a) through (f) below.yP(Y = y)yP(Y = y) D0.1890.04710.2886.0.03520.26570.00830.09780.02640.045

It is given that the random variable Y be the number of major hurricanes. The table shows the probability distribution for y.a. The notation that represent the event that the year had at least one major hurricane is Y≥1. Correct Answer: Option A.b. The notation that represent the event that the year had exactly eight major hurricane is Y=8. Correct Answer: Option B.c. The notation that represent the event that the year had between 6 and 8 major hurricane is 6≤Y≤8. Correct Answer: Option A.d. The probability distribution to determine the probability that the year had at least one major hurricane is, PY≥1=PY=1+PY=2+PY=3+PY=4+PY=5+PY=6+PY=7+PY=8=0.189+0.288+0.265+0.097+0.045+0.047+0.035+0.008+0.026=0.811 Thus, the probability distribution to determine the probability that the year had at least one major hurricane is 0.811.e. The probability distribution to determine the probability that the year had exactly eight major hurricanes is, PY=8=0.026 Thus, the probability distribution to determine the probability that the year had exactly eight major hurricanes is 0.026.f. The probability distribution to determine the probability that the year had between 6 and 8 major hurricanes, inclusive is, P6≤Y≤8=PPY=6+PY=7+PY=8=0.035+0.008+0.026=0.069 Thus, the probability distribution to determine the probability that the year had between 6 and 8 major hurricanes, inclusive is 0.069.