Suppose balls are drawn at random, one by one, without replacement from a box with 6 red and 4 black balls? (a) Given that there are exactly 2 red balls drawn in the first four draws, what is the conditional probability that the fifth draw yields a red ball? (b) What is the probability that a red ball is drawn for the third time in the fifth draw? (Hint: use the result in part (a) and the multiplication principle.)

A flush in the card game of poker occurs if a player gets five cards that are all the same suit (clubs, diamonds, hearts, or spades). Complete parts (a) through (c) to obtain the probability of being dealt a flush in five cards. C (a) Initially concentrate on one suit, say diamonds. There are 13 diamonds in a deck. Compute P(five diamonds) = P(first card is diamonds and second card is diamonds and third card is diamonds and fourth card is diamonds and fifth card is diamonds). In a standard 52-card deck, P(five diamonds) = (Round to six decimal places as needed.) (b) A flush can occur if a player receives five clubs or five diamonds or five hearts or five spades. Compute P(five clubs or five diamonds or five hearts or five spades). Note that the events are mutually exclusive. In a standard 52-card deck, P(five clubs or five diamonds or five hearts or five spades) = (Round to three decimal places as needed.) (c) A royal flush in the game of poker occurs if the player gets the cards Ten,…

In a lottery game, a single ball is drawn at random from a container that contains 25 identical balls numbered from 1 through 25. Use the equation P(AUB)=P(A) + P(B)-P(ANB), where A and B are any events, to compute the probability that the number drawn is prime or greater than 9. t The probability that the number drawn is prime or greater than 9 is (Type an integer or a decimal.) an example Get more help. 20 F3 $ 4 DOD F4 % 5 F5 A 6 MacBook Air. & 7 F7 C... * 8 ▶11 F8 9 ▶▶ F9 Clear all F10 4) Check answer F11 888 F12

A flush in the card game of poker occurs if a player gets five cards that are all the same suit (clubs, diamonds, hearts, or spades). Complete parts (a) and (b) to obtain the probability of being dealt a flush in five cards. (a) Initially concentrate on one suit, say clubs. There are 13 clubs in a deck. Compute P(five clubs) = P(first card is clubs and second card is clubs and third card is clubs and fourth card is clubs and fifth card is clubs). P(five clubs) = (Round to six decimal places as needed.)