Question

A bag contains 5 white and 10 red balls. Three balls are taken out at random. What is the probability of getting that all the three balls are red?​

Answer 1

Answer:

probability of getting that all the three ball are red=number of outcome/total number of outcome

=3/15

=1/5

Step-by-step explanation:

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Answer 2

given 5 white balls and 10 red balls, find probability that three balls drawn are all red

Explanation:

1. let the required probability be P, the event where all balls drawn are red be E and all events where three balls are drawn be S.
2. Then we get,         $P(E)= \frac{n(E)}{n(S)}$                                                                             $n(E)-\ no.\ of\ ways\ to\ draw\ three\ red\ balls\\n(S)-\ total\ no.\ of\ ways\ to\ draw\ three\ balls$  
3. total no. balls in the bag is 15 and no. of red balls is 10, then we get,             $n(E)= _{3}^{10}\textrm{C}\ \ \ \ \ \ \ \ and\ \ \ \ \ \ \ \ n(S)=_{3}^{15}\textrm{C}\ \ \ \ \ \ \ \ \ \ \ \ (here\ _{r}^{n}\textrm{C} = \frac{n!}{r!(n-r)!})$    
4. hence,                                                                                                                               $P(E)=\frac{n(E)}{n(S)}=\frac{ _{3}^{10}\textrm{C}}{_{3}^{15}\textrm{C}} \\P(E)= \frac{24}{91}= 0.26\ (approx)$