One card is selected at randon from an ordinary deck of 52 playing cards. Let  A= event a face card is selected, B=event a king is selected, and C= event a heart is selected  Q: what is P(A | (not B))

a). A girl is randomly picking flowers in a meadow for a bouquet. She will stop once she has picked 4 dandelions. Suppose that a randomly selected flower is a dandelion with probability 0.70. Find the probability that her bouquet will have exactly 8 flowers in total. b). An entomologist has a collection of 20 insect specimens: 5 are butterflies and 15 are moths. He randomly selects a sample of 6 specimens to study. Find the probability that the sample contains an equal number of butterflies and moths. 2

4) One number is randomly picked from 1 to 120. a) How many numbers are multiple of 3 or multiple of 5, or both? b) What is the probability to pick TWO numbers (no repeats), which are both "multiples of 3, but not multiples of 5?" Answer in (1 in ___)

By mistake six burned out light bulbs (B) have been mixed up with 4 good (G) ones. If a random sample of three is drawn, what is the probability a) that all will be good? b) at least 1 is burned out? c) at most 2 are burned out? d) Show the arithmetic of the probability that exactly 2 are good and 1 is bad.

4.) Find the probability of getting the following 5-card poker hands. (a) A royal flush (A, K, Q, J, 10 of a single suit.) (b) A straight (5 cards in a row, not all of the same suit, with ace either high or low) c) Three of a kind (exactly 3 cards of the same kind) (d) Exactly 2 different suits

Consider a collection of envelopes consisting of 1 red envelope, 1 blue envelope, 3 green envelopes, and 3 yellow envelopes. If two envelopes are selected at random, with replacement, determine the probability that both are red envelopes. The probability that both envelopes are red is (Type an integer or a simplified fraction.)

A card is randomly drawn from a deck of well-shuffled playing cards. Let event E be that the card is a king and event F be that the card is a diamond. A standard 52-card deck is split evenly into four suits of cards (hearts, diamonds, clubs, and spades). Each suit contains the cards ace, 2, 3.., 10, jack, queen, king. a) Find P(E) and P (E'). b) Find P(F) and P (F'). c) Find P(EUF).