Answer:
A.) About 90
Step-by-step explanation:
From the given table, the biologist tagged 150 trout. Also, he recaptured a total of 100 trouts of which 60 were recaptured with tags.
Thus, let the trout population in the lake be represented by x,
=
Cross multiply to have;
100 × x = 60 × 150
100x = 9000
Divide both sides by 100,
x =
= 90
Therefore, the trout population is about 90 in the lake.
I'm assuming a 5-card hand being dealt from a standard 52-card deck, and that there are no wild cards.
A full house is made up of a 3-of-a-kind and a 2-pair, both of different values since a 5-of-a-kind is impossible without wild cards.
Suppose we fix both card values, say aces and 2s. We get a full house if we are dealt 2 aces and 3 2s, or 3 aces and 2 2s.
The number of ways of drawing 2 aces and 3 2s is
and the number of ways of drawing 3 aces and 2 2s is the same,
so that for any two card values involved, there are 2*24 = 48 ways of getting a full house.
Now, count how many ways there are of doing this for any two choices of card value. Of 13 possible values, we are picking 2, so the total number of ways of getting a full house for any 2 values is
The total number of hands that can be drawn is
Then the probability of getting a full house is