OpenStudy (anonymous):

A bag contains two red marbles and five blue marbles. You draw a marble, record its color, replace it, and then draw a second marble. What is the probability that you draw a blue marble AT LEAST once? A) 0.28 B) 0.49 C) 0.71 D) 0.92

3 years ago
ganeshie8 (ganeshie8):

hint : \(P(blue ~"atleast"~ once) = 1 - P(not~blue~both~times) \)

3 years ago
OpenStudy (kropot72):

The probability of drawing two blue marbles is given by \[P(2\ blue)=\frac{5}{7} \times\frac{5}{7}=\frac{25}{49}\] The probability of drawing one blue marble is given by \[P(1\ blue)=\frac{5}{7} \times\frac{2}{7}=\frac{10}{49}\] The probability of drawing a blue marble at least once is therefore given by \[P(2\ blue)+P(1\ blue)=\frac{25}{49}+\frac{10}{49}=\frac{35}{49}=0.71\]

3 years ago
ganeshie8 (ganeshie8):

check ur \(P(1 blue)\) again, it should be : \(\large P(1\ blue)=\frac{5}{7} \times\frac{2}{7} + \frac{2}{7} \times \frac{5}{7} =2\times \frac{10}{49} \)

3 years ago
ganeshie8 (ganeshie8):

you can get blue either on first draw or second draw

3 years ago
OpenStudy (kropot72):

@ganeshie8 Of course, you are correct. So the result of this method is the same as for yours. \[\frac{25}{49}+\frac{20}{49}=\frac{45}{49}=0.92\]

3 years ago