Suppose that two integers from the set of 8 integers {1,2,… ,8} are choosen at random. Find the probability that i.5 and 8 are picked.
ii. Both numbers match.
iii. Sum of the two numbers picked is less than 4.

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 total outcomes.

Item i:

Two outcomes result in 5 and 8 being picked, (5,8) and (8,5), hence:

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:

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:

0.046875 = 4.6875% probability that the sum of the two numbers picked is less than 4.

A similar problem is given at link

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

what do you need me to answer?

step-by-step explanation: