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Answer:
See the attached photo for the calculations and answers
Step-by-step explanation:
The calculations and explanations are shown in the 3 attached photos below.



The answer to the given question will be a) P(flush) = 0.0019 b) P(one pair) = 0.4225 c) P( two pairs) = 0.475 d) P(three of a kind) = 0.211 e) P(four of a kind) = 0.00024
What is probability?
It's a field of mathematics that studies the probability of a random event occurring. From 0 to 1, the value is expressed.
The probability of being dealt a flush:
For a suit there are 4 choices and 13C₅ choices for a card in that suit
Probability of flush = 4.( 13C₅)/52C₅
Probability of flush = 0.0019
The probability of being dealt one pair:
There are 13 possible values of a, 4C₂ choice for suit of a, 12C₃ value for b, c, d and 4 choices each for choosing the suit of b, c, d.
P(one pair) = (13.4C₂.12C₃.4.4.4)/52C₅
P(one pair) = 0.4225
The probability of being dealt two pairs:
There are 13C₂ possibility for the value of a and b, 4C₂ choices for suits of both a and b and 44 possibilities for c from the remaining cards.
P(2 pairs) = (13C₂.4C₂.4C₂.44)/(52C₅) = 0.475
The probability of being dealt three of a kind:
There are 13 possibilities for the value of a and 4C₃ choices for the suits of a, 12C₂ possibilities for both b and c and 4 choices of suits for both b and c.
P( three of a kind) = (13.4C₃.12C₂.4.4)/52C₅ = 0.211
The probability of being dealt four of a kind:
There are 13 possibilities of a and 4C₄ values for the suit of a and 48 choices of b from the remaining cards.
P(four of a kind) = (13.4C₄.48)/52C₅ = 0.00024
Learn more about probability on:
https://brainly.com/question/24756209
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