Hi, can someone please help me with and explain these questions. Thank You!

1) In a test for ESP (extrasensory perception), a subject is told that the experimenter's cards, which he cannot see, contain either a star, a circle, a wave, a square, or a pyramid. As the experimenter looks at each of 10 cards in turn, the subject names the shape on the card. A subject who is just guessing has probability 0.20 of guessing correctly on each card.

• What is the probability that the subject guesses the shape correctly on two out of the 10 cards? (Round answer to 3 decimal places.)

2) Each symbol in a ciphertext has probability 0.01 of being used and symbols are independent of each other. Each line in a ciphertext has 35 symbols. Suppose that symbols D and E exist in the ciphertext. What is the theoretical mean number of times a D OR an E occurs in three lines of the text?

3) Antibiotic resistance occurs when disease-causing microbes become resistant to antibiotic drug therapy. Because this resistance is typically genetic and transferred to the next generations of microbes, it is a very serious public health problem. According to the CDC, approximately 32% of gonorrhea cases tested in a year were resistant to at least one of the three major antibiotics commonly used to treat gonorrhea. A physician treated 7 cases of gonorrhea during one week.

• What is the probability that exactly one out of the 7 cases was resistant to at least one of the three major antibiotics? (Round your answer to four decimal places.) P(X=1) =
• What is the probability that exactly two out of the 7 cases were resistant to at least one of the three major antibiotics? (Round your answer to four decimal places.) P(X = 2) =
• Also find the probability that one or more out of the 7 were resistant to at least one of the three major antibiotics. (Hint: It is easier to first find the probability that exactly zero of the 7 cases were resistant. Round your answer to four decimal places.) P(X 1) =