Answer:
There are 3744 possible full house hands in five-cards poker.
There are 5148 possible flush hands in five-cards poker.
Step-by-step explanation:
For a full house, we have to have 2 out of 4 of the same value with 13 different values, plus 3 out of 4 of the same value with 12 different values (because one was used for the first 2 cards). We can count those different options by using combinatorics (choosing 3 out of 4 and (in probability, and means those two are independent, meaning we multiply the options) 2 out of 4) and multiplying them by the different options of values:
In order to count how many hands result in a flush, we do it the same way, but now, we have to choose 5 out of 13 cards, times 4 possible suits:
Answer:
a) Alternative hypothesis should be one sided. Because Null and Alternative hypotheses are:
: μ=2.66 dyne-cm.
: μ<2.66 dyne-cm.
b) the hypothesis that mean adhesion is at least 2.66 dyne-cm is true
Step-by-step explanation:
Let μ be the mean adhesion in dyne-cm.
a)
Null and alternative hypotheses are:
: μ=2.66 dyne-cm.
: μ<2.66 dyne-cm.
b)
First we need to calculate test statistic and then the p-value of it.
test statistic of sample mean can be calculated as follows:
t= where
- M is the mean adhesion assumed under null hypothesis (2.66 dyne-cm)
- s is the standard deviation known (0.7 dyne-cm_2)
Sample mean is the average of 2.69, 5.76, 2.67, 1.62 and 4.12 dyne-cm, that is ≈ 3.37
using the numbers we get
t= ≈ 2.27
The p-value is ≈ 0.043. Taking significance level as 0.05, we can conlude that sample proportion is significantly higher than 2.66 dyne-cm.
Thus, according to the sample the hypothesis that mean adhesion is at least 2.66 dyne-cm is true
Answer:
Answer is 3/4
Step-by-step explanation:
Edward can distrubute pearls to 2 identical bags as fallows:
- 2W for one bag and 2B for another bag. In this scenerio the probability of picking a black pearl is 1/2.
- 1W and 1B for one bag and 1W and 1B for another bag. In this situation the probability of picking a black pearl is 1/2 × 1/2 is equal to 1/4
- At the end, the sum of two scenerio is 1/2 + 1/4 = 3/4
Answer:
20
Step-by-step explanation:
pq + 4
Given:
p = 4
q = 4
We plug the numbers in:
pq + 4
4(4) + 4
16 + 4
20