A bag contains 4 b l u e marbles, 3 w h i t e marbles, and 10 r e d marbles. If a marble is drawn from the bag, replaced, and another marble is drawn, what is the probability of drawing first a b l u e marble and then a r e d marble?

Accepted Solution

Answer:40/289Step-by-step explanation:We can see these two events are independent as Regina replaced marble after drawing one marble.We can find possible outcomes by adding number of blue, red and yellow marbles.possible outcomes= 4+3+10= 17Let us find probability of getting a blue marble on first draw.[tex]P( blue\ marble)= \frac{4}{4+3+10} = \frac{4}{17}[/tex]Now we will find probability of getting red marble.[tex]P(red/marble)= \frac{10}{17}[/tex]We can find probability of getting a blue marble and then red marble by multiplying both probabilities. [tex]P(\text{ Blue then red})=\frac{4}{17}* \frac{10}{17} =\frac{40}{289}[/tex]