MATH SOLVE

4 months ago

Q:
# an opaque bag contains 5 green marbles, 3 blue marbles, and 2 red marbles. if two consecutive marbles are drawn without replacement what is the probability that the first one will be green and the second one red? a. 0.51b. 0.10c. 0.11d. 0.16

Accepted Solution

A:

Answer:Option c. 0.11Step-by-step explanation:we know that
The probability of an event is the ratio of the size of the event space to the size of the sample space. The size of the sample space is the total number of possible outcomes The event space is the number of outcomes in the event you are interested in. so Let
x------> size of the event space
y-----> size of the sample space so
[tex]P=\frac{x}{y}[/tex]
In this problem we have thatTwo consecutive marbles are drawn without replacementstep 1Find out the probability that the first one will be green[tex]x=5[/tex]
[tex]y=5+3+2=10[/tex]
substitute
[tex]P=\frac{5}{10}=\frac{1}{2}[/tex]
step 2Find out the probability that the second one will be red[tex]x=2[/tex]
[tex]y=4+3+2=9[/tex]
substitute
[tex]P=\frac{2}{9}[/tex]
step 3Find out the probability that the first one will be green and the second one redMultiply both probabilities[tex](\frac{1}{2})(\frac{2}{9})=\frac{1}{9}=0.11[/tex]