Probability: 15 points! 3 Questions!! (answer be fractions in LOWEST TERMS)

1. If you roll two fair six-sided dice, what is the probability that the dice show the same number?

2. You flip a dime three times. Find the probability that all flips will land on tails.

3. A letter from the word MATH is chosen at random, then two coins are flipped. What is the probability of choosing the letter 'm' then getting two tails?

Find the magnitude, correct to two decimal places, made by each of the following with positive direction of the x axis a) y= x the answer is 45° but i don’t know how

In a test for esp (extrasensory perception), the experimenter looks at cards that are hidden from the subject. each card contains either a star, a circle, a wave, a cross or a square.(five shapes) as the experimenter looks at each of 20 cards in turn, the subject names the shape on the card. when the esp study described above discovers a subject whose performance appears to be better than guessing, the study continues at greater length. the experimenter looks at many cards bearing one of five shapes (star, square, circle, wave, and cross) in an order determined by random numbers. the subject cannot see the experimenter as he looks at each card in turn, in order to avoid any possible nonverbal clues. the answers of a subject who does not have esp should be independent observations, each with probability 1/5 of success. we record 1000 attempts. which of the following assumptions must be met in order to solve this problem? it's reasonable to assume normality 0.8(1000), 0.2(1000)%30 approximately normal 0.8(1000), 0.2(1000)% 10 approximately normal srs it is reasonable to assume the total number of cards is over 10,000 it is reasonable to assume the total number of cards is over 1000

Afamily went out to dinner and their bill was $113.if they want to leave a 19% tip, how much should they leave.