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Answer:
P(D|A)=0.666
Step-by-step explanation:
We will use the tree diagram to understand these probabilities that is attached to the bottom of this answer.
Since there are three coins in the box, the probability of taking one in particular (the double-headed one, which is event D) is one third, which is equal to 0.333
Since the coin showed heads, the probability of it being a double-tailed coin is zero.
The Bayes theorem says that P(D|A) is the multiplication of P(D) and P(A), divided the probability of A happening by any means, happening D or not, which is the sum of all probabilities of A happening:
1)Rewrite the table:
70, 49, 34.3, 24.01, 11.807
2) write the quotient of each number by the number before & notice the value:
49/70= 0.7
34.3/49 = 0.7
24.01/34.3 =0.7
16.0807/24.01 = 0.67 ≈0.7
You notice this is a geometric progression with r 0.7
The last term in a GP =ar^(n-1)
a=70; r= 0.7 n-1= number of terms (days -1)
For last term = 1 ==> then 1=70(0.7)^(n-1)
1/70 = (0.7)^(n-1)
log(1/70) =log[(0.7)^(n-1) ==> log1 - log 70 = (n-1) log(0.7) & you will find that it need 11.92 days to equal on & to be less than it will necessitate 12 Days
3) Domain and Range of this function:
Last term = a₁.rⁿ⁻¹. let last term be y==> f(n) = y =70(0.7)ⁿ⁻¹
or f(n) = y = 70(0.7)ⁿ / 0.7==> f(n) = [(0.7)ⁿ ]/ 100.
This is a decreasing exponential function where the coefficient
raised to n is < 1.
The domain is for all n>= 0.
When n→∞, f(n)→0; For n=0==>f(n) =70. So the range of f(n) is:<=70
8.25/3 = $2.75 per ice cream
2.75 * 2 = $5.50
It would cost $5.50 for 2 ice cream