Can someone help me with my math please?
2 answers:
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Answer:
The probability that it will choose food #2 on the second trial after the initial trial = 0.3125
Step-by-step explanation:
Given - A lab animal may eat any one of three foods each day. Laboratory records show that if the animal chooses one food on one trial, it will choose the same food on the next trial with a probability of 50%, and it will choose the other foods on the next trial with equal probabilities of 25%.
To find - If the animal chooses food #1 on an initial trial, what is the probability that it will choose food #2 on the second trial after the initial trial?
Proof -
By the given information, we get the stohastic matrix
As we know that,
The matrix is a Markov chain
Let
The initial state vector be
we choose this initial vector because given that If the animal chooses food #1 on an initial trial.
Now,
∴ we get
Now,
∴ we get
∴ we get
The probability that it will choose food #2 on the second trial after the initial trial = 0.3125
The value of x based on the tangent-secant theorem is: <u> 19.</u>
<em><u>Recall</u></em>:
- The secant-tangent theorem states that when a tangent and a secant meet outside a circle, the product of the secant length and it's segment outside the circle is equal to the square of the tangent segment length.
- Applying the tangent-secant theorem or rule, we will have this equation:
AB =
EB = 4
- Substitute:
- Add 12 to both sides
- Divide both sides by 4
x = 19
Therefore the <u>value of x is 19.</u>
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