Question

3.) A card game uses 36 cards, numbered 1-9 in four suits (clubs, diamonds, hearts, and spades). The cards are dealt to players so that each player has a hand of 9 cards. how many different 9-card hands are possible? Jules plays this game and recieves a hand with no hearys cards ar all. What is the proabability that a 9-card hand in this game would have 0 hearts?

4.) Micheala has an MP3 players randomly select a song for her to listen to. her playlist consists of 72 techno songs, 36 country songs, and 54 jazz songs. micharla plans to listen to 18 songs. which is the best predictiok for the number of tumes that Micheala will listen to a country song?

a. exactly 4 times b. close to 4 times, but probably not exactly 4 times c. exactly 6 times d. close to six times but probably not exactly 15 times

Answer #1

3) We have 36 cards. So 9 of these can be dealt in 36C9 ways ie
36!/(9!*27!)= **94,143,280**

There are 9 heart cards so 27 non heart cards. To get 0 hearts, we can do it in 27C9 ways = 27!/(9!*18!)= 4,686,825

So required Probability of getting no heart cards=
4,6868,825/94,143,280= **0.0498**

4) There are total 72+36+54= 162 songs out of which 36 are country songs

So Probability of playing a country song= 36/162

We play n=18 songs

So expected number of country songs played= 18*36/162= 4

So option a) is correct

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