Respuesta :
Answer:
Ok so we have a set of 8 numbers {1,2,...,8}
a) 5 and 8 are picked.The probability here is:
In the first selection we can pick 5 or 8, so we have two possible outcomes out of 8 total outcomes, then the probability for the first selection is:
P = 2/8 = 1/4.
Now, if one of those numbers was picked in the first selection, only one outcome is possible in this second selection, (if before we picked a 5, here we only can pick an 8)
Then the probability is:
P = 1/8
The joint probability is equal to the product of the individual probabilities, so here we have:
P = (1/4)*(1/8) = 1/32 = 0.003
b) The numbers match:
In the first selection we can have any outcome, so the probability is:
P = 8/8 = 1
Now, based on the previous outcome, in the second selection we can have only one outcome, so here the probability is:
P = 1/8 = 0.125
The joint probability is p = 1/8
c) The sum is smaller than 4:
The combinations are:
1 - 1
1 - 2
2 - 1
We have 3 combinations, and the total number of possible combinations is:
8 options for the first number and 8 options for the second selection:
8*8 = 64
The probabilty is equal to the number of outcomes that satisfy the sentence divided by the total numberof outcomes:
P = 3/64 = 0.047
Using the probability concept, it is found that there is a:
i. 0.03125 = 3.125% probability that 5 and 8 are picked.
ii. 0.125 = 12.5% probability that both numbers match.
iii. 0.046875 = 4.6875% probability that the sum of the two numbers picked is less than 4.
A probability is the number of desired outcomes divided by the number of total outcomes.
In this problem, two integers are chosen from a set of 8, hence, there are [tex]8^2 = 64[/tex] total outcomes.
Item i:
Two outcomes result in 5 and 8 being picked, (5,8) and (8,5), hence:
[tex]p = \frac{2}{64} = 0.03125[/tex]
0.03125 = 3.125% probability that 5 and 8 are picked.
Item ii:
8 outcomes result in both numbers matching, (1,1), (2,2), ..., (8,8), hence:
[tex]p = \frac{8}{64} = 0.125[/tex]
0.125 = 12.5% probability that both numbers match.
Item ii:
Three outcomes result in a sum of less than 2, (1,1), (1,2), (2,1), hence:
[tex]p = \frac{3}{64} = 0.046875[/tex]
0.046875 = 4.6875% probability that the sum of the two numbers picked is less than 4.
A similar problem is given at https://brainly.com/question/15536019
