The probability she takes out exactly $2.50 is 7/40.
What is probability?
Probability deals with the occurrence of a random event. The chance that a given event will occur. It is the measure of the likelihood of an event to occur.The value is expressed from zero to one.
For the given situation,
Number of coins in Kia bag = 10 coins
Number of $1 coins = 3
Number of 50 pence coins = 7
Kia takes at random 3 coins from the bag and the number of ways are
[tex]10C_{3} =\frac{(10)(9)(8)}{(1)(2)(3)}[/tex]
⇒ [tex]10C_{3} =\frac{720}{6}[/tex]
⇒ 120
Kia takes out exactly $2.50
So the combination could be two $1 coins and one 50 pence coins,
⇒ [tex](3C_{2}) (7C_{1} )[/tex]
⇒ [tex](\frac{(3)(2)}{(1)(2)} )(7)[/tex]
⇒ 21
Thus the probability she takes out exactly $2.50 is P(E) = [tex]\frac{21}{120}[/tex]
⇒ 7/40
Hence we can conclude that the probability she takes out exactly $2.50 is 7/40.
Learn more about probability here
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