sharonahrens354
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A restaurant will select select 1 card from a bowl to win a free lunch. Jimmy put in 10 cards in the bowl. The bowl has a total of 150 cards in it when they do the drawing. What are the odds of Jimmy winning A. 3/20 B. 1/150. C. 1/15. D. 1/10​

Respuesta :

if he put 10 in the bowl and there are 150 cards, the chance for him to win would be 10/150.
now by simplifying it, you get 1/15.
therefore answer is C
Cricetus

The odds of Jimmy winning will be "[tex]\frac{1}{15}[/tex]".

Let,

  • A be on the event of a random experiment [tex]P(A): P(\bar{A})[/tex] is considered as odds in favor of event A.
  • Odds in favor of an event A be [tex]m:n[/tex]
  • [tex]P(A) =P[/tex]
  • [tex]P(\bar{A}) = 1-P[/tex]

→ [tex]P(A):P(\bar{A}) = m:n[/tex]

       [tex]P:1-P = m: n[/tex]

→      [tex]\frac{P}{1-P} = \frac{m}{n}[/tex]

→        [tex]nP = m(1-P)[/tex]

               [tex]= m-mp[/tex]

               [tex]= nP+mP[/tex]

[tex](-m+n)= m[/tex]  

            [tex]P=\frac{m}{m+n}[/tex]

then,

→ Odds of Jimmy winning a free lunch P(A) will be:

= [tex]\frac{Number \ of \ cards \ Jimmy \ put \ in \ bowl}{Total \ Number \ of \ cards \ in \ bowl}[/tex]

= [tex]\frac{m}{m+n}[/tex]

= [tex]\frac{10}{150}[/tex]

= [tex]\frac{1}{15}[/tex]

Thus the above answer i.e., option C is the correct answer.

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