a jar has an equal number of red (r), blue(b), orange (o), yellow (y), and green (g) marbles. a marble is…

a jar has an equal number of red (r), blue(b), orange (o), yellow (y), and green (g) marbles. a marble is picked randomly and replaced. then another marble is picked from the jar. the organized list shows the possible outcomes. sample space rr br or yr gr rb bb ob yb gb ro bo oo yo go ry by oy yy gy rg bg og yg gg if you repeat this experiment 150 times, how many repetitions do you predict will result in picking at least one blue marble? 54 25 60 36

a jar has an equal number of red (r), blue(b), orange (o), yellow (y), and green (g) marbles. a marble is picked randomly and replaced. then another marble is picked from the jar. the organized list shows the possible outcomes. sample space rr br or yr gr rb bb ob yb gb ro bo oo yo go ry by oy yy gy rg bg og yg gg if you repeat this experiment 150 times, how many repetitions do you predict will result in picking at least one blue marble? 54 25 60 36

Answer

Explanation:

Step1: Find total number of outcomes

There are 5 colors of marbles. When picking two - marbles with replacement, the total number of outcomes in the sample space is $5\times5 = 25$ (by the multiplication principle).

Step2: Find number of outcomes with no blue marbles

If we exclude blue marbles, there are 4 colors. The number of outcomes with no blue marbles when picking two marbles is $4\times4=16$.

Step3: Find number of outcomes with at least one blue marble

The number of outcomes with at least one blue marble is the total number of outcomes minus the number of outcomes with no blue marbles. So, $25 - 16=9$.

Step4: Calculate the predicted number of repetitions

The probability of getting at least one blue marble in a single trial is $\frac{9}{25}$. If the experiment is repeated 150 times, the predicted number of repetitions with at least one blue marble is $150\times\frac{9}{25}=54$.

Answer:

54