Homework #1-4: One card is selected at random from a standard deck of playing cards. Determine the probability of: P (A or B). Hint use the formula: P(A or B) = P(A) P(B) – P(A and B) 1. A = an ace B = a jack P(ace) = 4/52 = 1/13 P(jack) = 4/52 = 1/13 P(ace and jack) = 0/52 = 0 as there is no card that is both an ace and a jack P(ace or jack) = P(ace) + P(jack) – P(ace and jack) = 1/13 + 1/13 - 0 = 2/13 Answer: 2/13 3. A = an ace B = a diamond P(ace) = 4/52 P(diamond) = 13/52 P(ace and diamond) = 1/52 (this is counting the ace of diamonds) P(ace or diamond) = P(ace) + P(diamond) – P(ace and diamond) = 4/52 + 13/52 - 1/52 Answer: 16/52 = 4/13 Homework #5-8 use the formula P(A or B) = P(A) + P(B) – P(A and B) to answer the following. 5) If P(A) = 0.5 and P(B) = 0.6 and P(A and B) = 0.2 find P(A or B) P(A or B) = P(A) + P(B) – P(A and B) = 0.5 + 0.6 – 0.2 Answer: 0.9 7) If P(A or B) = 0.8, P(A) = 0.5, P(B) = 0.6 find P(A and B) P(A or B) = P(A) + P(B) – P(A and B) 0.8 = 0.5 + 0.6 – P(A and B) 0.8 = 1.1 – P(A and B) -1.1__-1.1 -0.3 = -P(A and B) Answer: P(A and B) = 0.3 Homework: #9 – 12: a single dice is rolled one time. Find the probability of rolling 9) An odd number or a number greater than 2 P(odd number or a number greater than 2) = P(odd) + P(>2) – P(odd and >2) = 3/6 + 4/6 - 2/6 Answer: 5/6 11) A number less than 3 or greater than 5 P(< 3 or > 5) = P(<3) + P(>5) – P(< 3 and > 5) = 2/6 + 1/6 - 0/6 Answer: 3/6 = ½ 13) A jack or a diamond P(jack) = 4/52 P(diamond) = 13/52 P(jack and diamond) = 1/52 (this is counting the jack of diamonds) P(jack or diamond) = P(jack) + P(diamond) – P(jack and diamond) = 4/52 + 13/52 - 1/52 Answer: 16/52 = 4/13 15) A seven or a six P(seven) = 4/52 = 1/13 P(six) = 4/52 = 1/13 P(seven and six) = 0/52 = 0 as there is no card that is both a seven and a six P(seven or six) = P(seven) + P(six) – P(seven and six) = 1/13 + 1/13 - 0 = 2/13 Answer: 2/13 17) A red card or a ten P(red) = 26/52 P(ten) = 4/52 P(red and ten) = 2/52 (this is counting the ten of diamonds and hearts) P(red or ten) = P(red) + P(ten) – P(red or ten) = 26/52 + 4/52 - 2/52 Answer: 28/52 = 7/13 Homework #19 – 22: One marble is selected from a bag that contains 4 red, 5 white, 6 blue and 2 yellow. Find the probability of selecting 19) A red or a white P(red or white) = P(red) + P(white) – P(red and white) 4/17 + 5/17 - 0/17 Answer: 9/17 21) A blue or a white P(blue or white) = P(blue) + P(white) – P(blue and white) 6/17 + 5/17 - 0/17 Answer: 11/17 Homework #23 – 26: The numbers 1, 2, 3, 4, …., 14 are placed on a piece of paper and thrown into a bucket. One piece of paper is randomly selected. What is the probability that: 23) The number is odd or greater then 7 P(odd or > 7) = P(odd) + P(> 7) – P(odd and > 7) 7/14 + 7/17 - 3/14 Answer: 11/14 25) The number is greater than or equal to 5 or even Homework #27-30: The letters of the word Mississippi are placed on pieces of paper and thrown into a bucket. One piece of paper is randomly selected. What is the probability that: 27) The letter is a p or an m? P(p or m) = P(p) + P(m) – P(p or m) 2/11 + 1/11 – 0-11 Answer: 3/11 29) The letter is a vowel or alphabetically after r? Hint there are 4 vowels (iiii) There are 4 letters alphabetically after r (ssss) There are no letters that are vowels and after r P(vowel or after r) = P(vowel) + P(after r) – P(vowel and after r) 4/11 + 4/11 - 0/11 Answer: 8/11 .