MATH: statistic/ probalitity - need help problem with #9-19 (a-c, a-b) - related

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MATH: statistic/ probalitity
- need help problem with #9-19 (a-c, a-b)
- related questions
- please explain/show steps/answer to the question

Avery has been learning to play some new card games and is curious about the probabilities of being dealt different cards from a standard 52-card deck. Help hi figure out the probabilities listed below a. What are P(king), P(queen), and P(club)? b. What is P(king or club)? How does your answer relate to the probabilities you calculated in part (a)? probabilities you calculated in part (a)? 01-19 Susannah is drawing a card from a standard 52-card deck. a. What is the probability that the card she draws a card that is less than 5? b. What is the probability that the card she draws is a red card (diamond or heart) or a face card?

Explanation / Answer

There are 52 cards, one card can be selected in 52C1.

a)
P(King) = 4C1/52C1 = 4/52 = 1/13
P(Queen) = 4C1/52C1 = 4/52 = 1/13
P(club) = 13C1/52C1 = 1/4

b)
There are 16 (13 + 4 - 1) cards which are king or club.

P(king or club) = 16C1/52C1 = 16/52 = 4/13

from part a)
P(King) + P(club) - P(King and Club)
= 1/13 + 1/4 - 1/52 = 4/13

c)
There are 8 cards (4+4) which are king or queen.

P(king or queen) = 8/52 = 2/13

From part a) P(king) + P(queen) = 1/13 + 1/13 = 2/13

9-19
a)
There are 4*4 = 16 cards which are less than 5

P(less than 5) = 16C1/52C1 = 16/52 = 4/13

b)
26 red cards
12 face cards
6 face cards which are red

Required probability = (26 + 12 - 6)/52 = 32/52 = 8/13

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