Find the probability

Probability Level 2

Twenty dancers from a particular dance school take part in the national dance championships. All of the 20 enter in either solo events or team events or both solo and team. Five of the 20 do not enter in solo events and two do not enter in team events. If one of the 20 dancers is randomly selected to represent the school in the opening ceremony, what is the probability that this dancer is one who enters in both solo and team events?

13 20 \frac {13}{20} 2 20 \frac 2{20} 5 20 \frac 5{20} 2 13 \frac 2{13}

Sanjoy Roy by Sanjoy Roy , 30, Bangladesh

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1 solution

Zee Ell
Aug 23, 2016

Since 5 dancers do not participate in solo events and 2 do not participate in team events, therefore

the number of dancers doing both solo and team events:

20 - 5 - 2 = 13

and the probability sought by us:

Number of dancers doing both solo and team events Total number of dancers = 13 20 \frac { \text {Number of dancers doing both solo and team events }}{\text {Total number of dancers}} = \boxed { \frac {13}{20} }

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