In a hand of 5 cards, you want 4 of them to be of the same rank, and the fifth can be any of the remaining 48 cards. So if the rank of the 4-of-a-kind is fixed, there are
possible hands. To account for any choice of rank, we choose 1 of the 13 possible ranks and multiply this count by
. So there are 624 possible hands containing a 4-of-a-kind. Hence A occurs with probability

There are 4 aces in the deck. If exactly 1 occurs in the hand, the remaining 4 cards can be any of the remaining 48 non-ace cards, contributing
possible hands. Exactly 2 aces are drawn in
hands. And so on. This gives a total of

possible hands containing at least 1 ace, and hence B occurs with probability

The product of these probability is approximately 0.000082.
A and B are independent if the probability of both events occurring simultaneously is the same as the above probability, i.e.
. This happens if
- the hand has 4 aces and 1 non-ace, or
- the hand has a non-ace 4-of-a-kind and 1 ace
The above "sub-events" are mutually exclusive and share no overlap. There are 48 possible non-aces to choose from, so the first sub-event consists of 48 possible hands. There are 12 non-ace 4-of-a-kinds and 4 choices of ace for the fifth card, so the second sub-event has a total of 12*4 = 48 possible hands. So
consists of 96 possible hands, which occurs with probability

and so the events A and B are NOT independent.
Answer:
Around 1,500 pounds
Step-by-step explanation:
Because you said "estimate," I will be estimating this.
49% rounds up to 50%
3,025 rounds down to 3,000
50% of 3,000 is 1,500 pounds.
Skew lines are lines that are not pararell or perpendicular.
The only lines that fit this explanation are AE and GF
Hope this helps!
We conclude that 375 portions can be sold.
<h3>
How many portions can be sold?</h3>
We know that 500 portions have been ordered, but only 5/6 of that was delivered, so the number of delivered portions is:
p = (5/6)*500 = 416.6
Which we can round to the next whole number, 417.
Now we know that 10% of these are given to the players and staff, then the number of portions that can be sold is the 90% of 417, which is:
N = 417*(90%/100%) = 417*0.9 = 375
We conclude that 375 portions can be sold.
If you want to learn more about percentages:
brainly.com/question/843074
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2) C
3) B
4) C
6) I'm pretty sure its D but it could be C