+6 | Colour | yellow | black | red |
| Probability | 1/7 | ? | ? |
Daniel has a bag of marbles. he has twice as many black marbles as red marbles. the rest are yellow. he is going to take a marble at random from the bag. yellow is 1/7 what is black and red probability?
+118609 Colouryellowblackred
Probability1/7??
Daniel has a bag of marbles. he has twice as many black marbles as red marbles. the rest are yellow. he is going to take a marble at random from the bag. yellow is 1/7 what is black and red probability?
P(yellow) = 1/7
so
P(red or black) = 6/7
and there are twice as many black as red so that must be
P(red)=2/7
P(black)=4/7
+33616 n = b + r + y n = total
b = 2r twice as many black as red
y/n = 1/7 yellow probability
n = 3r + y
y/(3r + y) = 1/7
7y = 3r + y
6y = 3r
r = 2y
b = 4y
r/n = 2y/n = 2/7 probability of drawing a red
b/n = 4y/n = 4/7 probability of drawing a black
(I see Melody beat me to it. Luckily, I got the same results as her!).
.
+26367 Probability Question
| Colour | yellow | black | red |
| Probability | 1/7 | ? | ? |
Daniel has a bag of marbles. he has twice as many black marbles as red marbles.
the rest are yellow.
he is going to take a marble at random from the bag.
yellow is 1/7
what is black and red probability?
\(\begin{array}{|rcll|} \hline b=2r \\ \hline \end{array}\)
\(\begin{array}{|lcrcll|} \hline \text{Probability yellow } = \frac17 & \Rightarrow & y+b+r &=& 7 & \text{ and } \quad y = 1 \\ & & y+b+r &=& 7 & \qquad b=2r \quad y = 1 \\ & & 1+2r+r &=& 7 \\ & & 3r &=& 6 \\ & & \mathbf{ r } & \mathbf{=} & \mathbf{2} \\ \text{Probability red:} & & \mathbf{ \frac{r}{y+b+r} } & \mathbf{=} & \mathbf{\frac27 } \\\\ & & y+b+r &=& 7 & \qquad r=2 \quad y = 1 \\ & & 1+b+2 &=& 7 & \\ & & b &=& 7-3 & \\ & & \mathbf{ b } & \mathbf{=} & \mathbf{4} \\ \text{Probability black:} & & \mathbf{ \frac{b}{y+b+r} } & \mathbf{=} & \mathbf{\frac47 } \\\\ \hline \end{array} \)
\(\begin{array}{|l|r|r|r|} \hline \text{Colour} & \text{yellow} & \text{black} & \text{red} \\ \hline \text{Probability} & \frac17 & \frac47 & \frac27 \\ \hline \end{array} \)
