Respuesta :
Given:
5 blue marbles
3 white marbles
5 red marbles
TOTAL: 13 marbles in the bag
Solution:
a. Find the probability of picking a blue and then a red.
On the first pick, we know that there are 5 blue out of 13 marbles in the bag. On the second pick, there are 12 marbles left. Assuming that a blue marble was picked, there is now 5 red out of 12 marbles in the bag. So, the probability of picking a blue and then a red is:
[tex]P(blue)\times P(red)[/tex][tex]\frac{5}{13}\times\frac{5}{12}=\frac{25}{156}[/tex]The probability of picking a blue and then a red is 25/156.
b. A red and then a white
In the same way as the previous one, we know originally that there were 5 red marbles out of 13 marbles in the bag. Assuming that red marble was picked, we know that there are now 3 white marbles out of 12 marbles for the second pick. So, the probability of picking a red and then a white is:
[tex]\frac{5}{13}\times\frac{3}{12}=\frac{15}{156}[/tex]Reduce 15/156 by dividing both numerator and denominator by 3.
[tex]\frac{15\div3}{156\div3}=\frac{5}{52}[/tex]The probability of picking a red and then a white is 5/52.
c. A blue, then a blue, then a blue.
For the first pick, we have 5 blue marbles out of 13 marbles.
For the second pick, we now have 4 blue marbles out of 12 marbles.
For the third pick, we now have 3 blue marbles out of 11 marbles.
[tex]\frac{5}{13}\times\frac{4}{12}\times\frac{3}{11}[/tex][tex]\frac{5}{13}\times\frac{1}{3}\times\frac{3}{11}[/tex][tex]\frac{5}{13}\times\frac{1}{3}\times\frac{3}{11}=\frac{15}{429}[/tex]Reduced 15/429 by dividing both numerator and denominator by 3.
[tex]\frac{15\div3}{429\div3}=\frac{5}{143}[/tex]The probability of picking a blue, then a blue, then a blue is 5/143.
