two cards are chosen at random from a deck of 52 playing cards. what is the probability that they are both aces?
1 answer:
Answer:
The probability that they are both aces is 0.00452.
Step-by-step explanation:
Consider the provided information.
Out of 52 playing card we need to select only 2.
Thus, the sample space is:
Two cards are Ace.
The number of Ace in a pack of playing card are 4 and we need to select two of them.
This can be written as:
Thus, the probability that they are both aces is:
Hence, the probability that they are both aces is 0.00452.
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Answer:
Now we can calculate the p value with the following probability:
Since the p value is lower than the significance level we have enough evidence to reject the null hypothesis and we can conclude that the true proportion for this case is higher than 0.5
Step-by-step explanation:
Data given and notation
n=75 represent the random sample taken
estimated proportion of interest
is the value that we want to test
represent the significance level
Confidence=95% or 0.95
z would represent the statistic
represent the p value
System of hypothesis
We want to verify if the true proportion is higher than 0.5:
Null hypothesis:
Alternative hypothesis:
The statistic is given by:
(1)
Replacing the info given we got:
Now we can calculate the p value with the following probability:
Since the p value is lower than the significance level we have enough evidence to reject the null hypothesis and we can conclude that the true proportion for this case is higher than 0.5