Answer:
72.4%
Step-by-step explanation:
The probability of A occurring given that B occurs = the probability of both A and B / the probability of B
P(A|B) = P(A∩B) / P(B)
This can be rearranged as:
P(A∩B) = P(B) P(A|B)
In this case:
A = biased coin is chosen
~A = fair coin is chosen
B = 4 heads then 1 tail
First, let's find P(A∩B).
P(A∩B) = P(B) P(A|B)
P(A∩B) = ½ × ₅C₄ (⅘)⁴ (⅕)¹
P(A∩B) = 0.2048
Next, find P(~A∩B).
P(~A∩B) = P(B) P(~A|B)
P(~A∩B) = ½ × ₅C₄ (½)⁴ (½)¹
P(~A∩B) = 0.078125
Therefore, the probability that the coin is biased is:
P = P(A∩B) / (P(A∩B) + P(~A∩B))
P = 0.2048 / (0.2048 + 0.078125)
P = 0.723866749
The probability is approximately 72.4%.
Answer:
There's an option to insert pictures. You have to click on a 'paper pin' like symbol
Step-by-step explanation:
See, I've inserted one pic.
Step-by-step explanation:
Answer:
5 felt pads.
7 cards.
Step-by-step explanation:
Remark
- The total number of items is 12
- So let the felt sheets be x
- Let the cards = y
Equations and Solution
x + y = 12
Now the price is 7.75 that she has to pay for the 12 items. She wants to come back with 0 dollars.
0.5x + 0.75y = 7.75 Multiply this equation by 2
x + 1.5y = 15.50 write the first equation underneath and subtract.
<u>x + y = 12</u>
.5y = 3 Divide by 0.5
y = 3/0.5
y = 7
So she can get 7 cards.
x + y = 12
x + 7 = 12
x = 12 - 7
x = 5
So she can buy 5 felt pads.
Convert them to comparable thingummys
convert to fraction
percent means parts out of 100
30%=30/100=3/10
3/10 vvs 1/3
make bottom number 30
3/10 times 3/3=9/30
1/3 times 10/10=10/30
10/30>9/30
1/3 is bigger
