(a.) is the answr. ............................................
Answer: 26 cups will fit in a dispenser that is 30 cm high.
Step-by-step explanation:
First of all, we know that the first cup in the stack (the bottom cup) will be ten centimeters high, and we know that for every cup that is added on top of that, .8 centimeter will be added to the height. So, if we want to find how many cups will be in the dispenser we do this simple math:
30 - 10 = 20 Because the first cup is ten centimeters, we have to subtract that from the dispenser height.
20/.8=25 To find how many cups will be stacked on top of the first cup, we divide the remaining height by .8, the height of every other cup.
Now that we know that there will be 25 cups stacked on top of the first, we add the bottom cup to the rest of them.
25 + 1 = 26 Cups.
Normally when dealing with coins the probability of getting heads or tails is 0.5 each. However in this case since its an unfair coin, the probability of getting heads is 0.2.
H - head
T - tails
R - red marble
pr (H) = 0.2
urn
6 red and 4 blue
pr (T) = 0.8
urn
3 red and 5 blue
when heads is obtained
red - 6/10 -0.6
blue - 4/10 - 0.4
therefore when multiplying with 0.2 probability of getting heads
pr (R ∩ H) red - 0.6*0.2 = 0.12
when tails is obtained
red - 3/8 - 0.375
blue - 5/8 - 0.625
when multiplying with 0.8 probability of getting tails
pr (R ∩ T) red - 0.375 * 0.8 = 0.3
using bayes rule the answer can be found out,
the following equation is used;
pr (H | R) = pr (R ∩ H) / {pr (R ∩ H) + pr (R ∩ T)}
= 0.12 / (0.12 + 0.3)
= 0.12 / 0.42
= 0.286
the final answer is 0.286
