Thanks Ginger..... I think you made a couple of little mistakes :)
1)
a bag has 4 red ball's, 5 white ball's and 6 blue ball's. 3 ball's are drawn at random from the bag without putting it back. what is the probability that they are of the same color?
There are 4+5+6=15 b***s altogether.
What is the probability of drawing 3 red b***s
\(\text{The prob of 3 reds is }\frac{4}{15}\times \frac{3}{14} \times \frac{2}{13}=\frac{24}{2730}\\ \text{The prob of 3 whites is }\frac{5}{15}\times \frac{4}{14} \times \frac{3}{13}=\frac{60}{2730}\\ \text{The prob of 3 blues is }\frac{6}{15}\times \frac{5}{14} \times \frac{4}{13}=\frac{120}{2730}\\ \text{add all these together and you get}\\ \text{P(three the same colour )=}\frac{34}{455}\\\)
Another method:
\(\frac{\binom{4 }{3}\times \binom{5}{3}\times \binom{6}{3}}{\binom{15}{3}}=\frac{4+10+20}{455}=\frac{34}{455}\)
2)
2 cards are chosen at random from a standard deck of 52-card. what is the probability that the 1st card is a heart and the second card is a 10?
Mmm
10 of hearts followed by another 10
\(\frac{1}{52} \times \frac{3}{51} = \frac{3}{52*51}=\frac{3}{2652}\)
or
a heart that is not a 10 followed by a 10
\(\frac{12}{52}\times \frac{4}{51}=\frac{48}{2652}\\ ~\\ \text{P(heart then 10)}=\frac{3+48}{2652}=\frac{51}{2652}=\frac{1}{52}\)
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