Answer:
Hence, the probability of the NOT spinning a RED, flipping TAILS, and then NOT spinning and EVEN number is:
![\dfrac{2}{9}](https://tex.z-dn.net/?f=%5Cdfrac%7B2%7D%7B9%7D)
Step-by-step explanation:
The spinner contains three colors Red, Blue and Yellow.
Let P denote the probability of an event.
Let A denote the event that red color is not obtained on the spinner.
B denote the event that tail is obtained on flipping a coin.
and C denote the event that an odd number is not obtained on spinner.
Hence,
P(A)=2/3
( Since out of three choice 2 are not red)
P(B)=1/2
( Since the only outcomes are H and T which have equal chances to come up)
and
P(C)=2/3
( Since the number on the spinner are 1,2 and 3 out of which only one is even)
Clearly all the events are independent.
Hence, the probability of the compound event is:
![P(A)\cdot P(B)\cdot P(C)\\\\=\dfrac{2}{3}\cdot \dfrac{1}{2}\cdot \dfrac{2}{3}\\\\=\dfrac{2}{9}](https://tex.z-dn.net/?f=P%28A%29%5Ccdot%20P%28B%29%5Ccdot%20P%28C%29%5C%5C%5C%5C%3D%5Cdfrac%7B2%7D%7B3%7D%5Ccdot%20%5Cdfrac%7B1%7D%7B2%7D%5Ccdot%20%5Cdfrac%7B2%7D%7B3%7D%5C%5C%5C%5C%3D%5Cdfrac%7B2%7D%7B9%7D)