At a drug rehab center 23% experience depression and 38% experience weight gain. 12% experience both. If a patient from the center is randomly selected, find the probability that the patient A. experiences neither depression nor weight gain. B. experiences depression given that the patient experiences weight gain.   C.experiences weight gain given that the patient experiences depression.   D. Are depression and weight gain mutually exclusive? E. Are depression and weight gain independent? Hint Video on Probability Textbook Pages

An experiment consists of tossing a penny, a nickel and a dime. Of interest is the side the coin lands on. A. How many elements are there in the sample space? B. Let A be the event that there is at least one head and at least one tail. P(A) = C. Let B be the event that the first and second tosses land on heads. Are the events A and B mutually exclusive? Hint Textbook Pages

An experiment consists of tossing a nickel, a dime and a quarter. Of interest is the side the coin lands on. A. How many elements are there in the sample space? B. Let A be the event that there are at least two tails. P(A) = C. Let B be the event that the first and second tosses land on heads. Are the events A and B mutually exclusive? Hint Textbook Pages

Consider the following scenario: • Let P(C) = 0.7 • Let P(D) = 0.4 • Let P(C|D) = 0.8 A. P(C AND D) = B. Are C and D Mutually Exclusive?   C. Are C and D independent events? D. P(C OR D) = E. P(D|C) = Round your answer to two decimal places. Hint Textbook Pages

Roll two fair dice. Each die has six faces. A. Let A be the event that the first die is odd and the second is a 4, 5, or 6. P(A) = Present your answer as a decimal. B. Let B be the event that the sum of the two dice is a 10. P(B) = Round your answer to three decimal places. C. Are A and B mutually exclusive events? D. Are A and B independent events? Hint Example Video on Probability Textbook Pages

A special deck of cards has 10 cards. Four are green, three are blue, and three are red. When a card is picked, the color of it is recorded. An experiment consists of first picking a card and then tossing a coin. A. How many elements are there in the sample space? B. Let A be the event that a green card is picked first, followed by landing a head on the coin toss. P(A) = Present your answer as a decimal number. C. Let B be the event that a red or blue is picked, followed by landing a head on the coin toss. Are the events A and B mutually exclusive? D. Let C be the event that a green or blue is picked, followed by landing a head on the coin toss. Are the events A and C mutually exclusive? Hint Example Video on Probability Textbook Pages

An experiment consists of first rolling a die and then tossing a coin: A. How many elements are there in the sample space? B. Let A be the event that either a 1, 2, 3 or 4 is rolled first, followed by landing tails on the coin toss. P(A) = Present your answer as a decimal rounded to two decimal places. C. Let B be the event that an even number is rolled, followed by landing tails on the coin toss. Are the events A and B mutually exclusive? Hint Example Video on Probability Textbook Pages

J and K are independent events. P(J | K) = 0.23. Find P(J) Hint Textbook Pages

A special deck of cards has 20 cards. Nine are green, seven are blue, and four are red. When a card is picked, the color of it is recorded. An experiment consists of first picking a card and then tossing a coin. A. How many elements are there in the sample space? B. Let A be the event that a red card is picked first, followed by landing a tail on the coin toss. P(A) = Present your answer as a decimal number. C. Let B be the event that a green or blue is picked, followed by landing a tail on the coin toss. Are the events A and B mutually exclusive? D. Let C be the event that a green or red is picked, followed by landing a tail on the coin toss. Are the events A and C mutually exclusive? Hint Example Video on Probability Textbook Pages

Suppose that you have 11 cards. 5 are red and 6 are black. The cards are well shuffled. You randomly draw two cards with replacement. • R1 = first card drawn is red • R2 = second card drawn is red Hint Video on Independent Events Textbook Pages P(R1 AND R2) = Round your answer to two decimal places. P(At least one red) = Round your answer to two decimal places. P(R2|R1) = Round your answer to two decimal places. Are R1 and R2 independent?