00:01
This problem says a card is selected at random from a standard deck of 52 playing cards.
00:05
We're asked to find the probability of each event, and all of our probabilities are or scenarios, where a wants us to find the probability of randomly selecting a black suit or an ace, randomly selecting a diamond, or an eight for b, and for c, we want to know the probability of randomly selecting a6 or a face card.
00:20
So when we want the probability when we have an or scenario, we add the probabilities together of those two events happening individually, but then we look to see if there's any overlap between the two categories that we might need to subtract.
00:33
So for the probability of getting a black -suited card, we have clubs and spades.
00:38
So that makes up half of the 52 card deck.
00:40
So that would be 26 out of 52.
00:43
And then we would add the probability of getting an ace, and there's one ace for each suit.
00:48
So that's four possibilities there.
00:50
But there is overlap between the black -suited cards and the aces because we have an ace of spades and an ace of clubs.
00:57
So those cards got countered.
00:59
Both for being black suits and aces, so we have to subtract that overlap.
01:03
So they don't get counted twice.
01:05
So that would give us 26 plus 4 minus 2 or 28 out of 52 for our probability.
01:11
And then we can simplify by dividing numerator and denominator by 4, which would give us the simplified probability of 7 over 13 or 713s.
01:21
Next, we want the probability of getting a diamond or an 8, and diamond is one of the four suits in the decks.
01:27
That's one fourth of the cards, which would be 13 out of 15th.
01:30
And there's 1 8 for every suit...