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in the drawing six out of every 10 tickets are winning tickets of the winning tickets one out of every three awards is a larger prize what is the probability that a ticket is randomly chosen will award a larger prize

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MissPhiladelphia
the probability that a ticket is randomly chosen will award a larger prize can be solved knowing the probability of each event. Since the probability of a winning ticket is 6/ 10 then 1/3 is a larger prize. So for every 10 there 2 larger prize. So the probability that a ticket is randomly chosen will award a larger prize is 2/10 or 1/5

[tex]Answer: P(\text{a ticket is randomly chosen will award a large prize)}=\frac{2}{21}[/tex]

Since we have given that

Total number of tickets =10

Number of winning tickets =6

[tex]\text {Possibility of getting a winning ticket }=^{10}C_6[/tex]

In which one out of every three awards is a large prize

so,

[tex]\text{ Possibility of getting a large prize }=^6C_3[/tex]

Now,

[tex]P(\text{a ticket is randomly chosen will award a large prize)}=\frac{^6C_3}{^{10}C_6}\\\\=\frac{20}{210}\\\\=\frac{2}{21}[/tex]

[tex]P(\text{a ticket is randomly chosen will award a large prize)}=\frac{2}{21}[/tex]

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