1. You draw one card randomly from a standard deck of 52 playing cards (no jokers)

Event A: You draw a heart card.

Event B: You draw a card that is not a face card.

Event C: You draw a non-face card that is divisible by 3.

What is the probability that Event A, B, or C will occur?

2. Empirically verify the probability you calculated in Problem 1 with a Python program that simulates drawing randomly from a deck of cards. Initialize a list of cards, each card with a suit and a value. Generate a random number 0 through 51 to pick a card from the list. Check for Events A, B, and C. Repeat this a million times and count how many times Event A, B, or C occurred. After a million card picks, print your count divided by a million. How well does this simulation probability match the probability you calculated in Problem 9? Also print the simulation probabilities after 100; 1,000; 10,000; and 100,000 card picks. Determine how many simulated card picks are needed for the simulation probability to match your calculated probability to 3 decimal places.

For problems 5 and 6, The body temperatures of adults have a mean of 98.6 " F and a standard deviation of 0.60 * F. A random sample of 38 adults selected. 5. What is the approximate distribution of I = (the sample average of the 36 temperatures)? (Use Central Limit Theprem.) a) Normally distributed with u=98.6 and a = 0.50. C bl Normally distributed with =16.43 and o = 0.01 c Normally distributed with p=99.5 and o = 0.10 Normally distributed with p=98.6 and o = 0 01 6. Find the probability that their mean body temperature is greater than 98.4 . F. P ( x 7 980 ) a) -2.00 b) 2.00 98 2 _48. 97 90.0228 0.6772Table of the numbers of hits for 25 games 3 1 1 2 2 2 0 2 2 1 3 2 2 0 1 0 1 3 2 2 2 1 5 3 1 Table of the numbers of hits for 50 games 3 1 1 2 2 2 0 2 2 1 3 2 2 0 1 0 1 3 2 2 2 1 5 3 1 3 2 2 1 1 C 3 0 1 0 3 2 2 1 1 2 0 1 2 2 1 3 0 3