Question

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.

Answer 1

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