Each of two urns contains green balls and red balls. Urn one contains 10 green balls and 8 red balls. Urn two contains 3 green balls and 10 red balls. If a ball is drawn from each urn, what is P(red and red)?
A. 23/18
B. 10/27
C. 40/117
D. 18/31
The probability of drawing a red ball from urn one is $\frac{8}{18}=\frac{4}{9}$, and the probability of drawing a red ball from urn two is $\frac{10}{13}$. Therefore, the probability of drawing a red ball from both urns is $\frac{4}{9}\cdot\frac{10}{13}=\frac{40}{117}$. The answer is $\boxed{\textbf{(C) } 40/117}$.
if you spin the spinner below twice, what is P(vowel, then Q)?
There is a spinner with 6 spaces, 3 being vowels.
A.1/10
B.1/9
C.2/9
D.1/12
The probability of spinning a vowel on the first spin is $\dfrac{3}{6} = \dfrac12$. Since there are only 2 vowels on the spinner ($\text{A}$ and $\text{E}$), the probability of spinning $\text{Q}$ (which is not a vowel) on the second spin is $\dfrac{1}{6-1} = \dfrac15$. So, the probability of spinning a vowel and then $\text{Q}$ is $\left(\dfrac12\right)\left(\dfrac15\right) = \boxed{\dfrac1{10}}$ or A.
To find the probability of drawing a red ball from each urn, we need to multiply the probabilities of drawing a red ball from each urn together.
In the first urn, there are a total of 18 balls (10 green + 8 red). Therefore, the probability of drawing a red ball from the first urn is 8/18.
In the second urn, there are a total of 13 balls (3 green + 10 red). Therefore, the probability of drawing a red ball from the second urn is 10/13.
To find the probability of drawing a red ball from both urns, we multiply the probabilities:
P(red and red) = (8/18) * (10/13)
= 80/234
Simplifying the fraction, we get:
P(red and red) = 40/117
Therefore, the correct answer is C. 40/117.