Answer:
Hence, the probability of the NOT spinning a RED, flipping TAILS, and then NOT spinning and EVEN number is:
[tex]\dfrac{2}{9}[/tex]
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:
[tex]P(A)\cdot P(B)\cdot P(C)\\\\=\dfrac{2}{3}\cdot \dfrac{1}{2}\cdot \dfrac{2}{3}\\\\=\dfrac{2}{9}[/tex]
The P(compound), P(not spinning red), P(tail), and P(even) are [tex]\dfrac{1}{3}, \dfrac{2}{3}, \dfrac{1}{2},and\ \dfrac{2}{3} [/tex] respectively.
It is the ratio of the favorite events to the total number of events.
Total number of events = 3 (spin a spinner, flip a coin, spin a spinner and flip a coin )
Favorable event = 1 (spin a spinner and flip a coin)
[tex]\rm Probability = \dfrac{favorable\ event}{total\ number\ of\ events} [/tex]
For compound probability P(Compound)
[tex]\rm P(Compound) = \dfrac{1}{3} [/tex]
The probability of not spinning red will be
Favorable events = 2 (spinning of blue and yellow)
Total number of events = 3 (Spinning of red, yellow, and blue)
[tex]P(not\ spinning\ red) = \dfrac{2}{3} [/tex]
The probability of flipping tail
Favorable event = 1 (head or tail)
Total event = 2 (head and tail)
[tex]P(tail) = \dfrac{1}{2} [/tex]
The probability of not spinning of even number
Favorable events = 2 (1, 2, or 3)
Total number of events = 3 (1, 2, and 3)
[tex]P(even) = \dfrac{2}{3} [/tex]
Thus, the P(compound), P(not spinning red), P(tail), and P(even) are [tex]\dfrac{1}{3}, \dfrac{2}{3}, \dfrac{1}{2},and\ \dfrac{2}{3} [/tex] respectively.
To more about the Probability link is given below.
https://brainly.com/question/795909?
