Answer:
4. 4/13
5. 7/13
6. 4/13
Explanation:
A standard deck has 52 cards, 4 suits, each suit has cards Ace through 10 and the face cards, Jack, Queen, King.
If the idea of suits confuses you, think about Uno where the cards are blue, yellow, green, and red. Only here the suits are Diamonds, Clubs, Hearts, and Spades
To calculate compound probability use the following formula:
P(A ∪ B) = P(A) + P(B) - P(A | B)
This says that the probability of A or B occuring is the probability of A, plus the probability of B, minus the probability of them both occuring at the same time.
4) Randomly selecting a diamond or a seven.
There are 13 diamonds in a deck and 4 sevens, one from each suit. The joint event for this probabaility is randomly drawing a 7 of diamonds. There is only one of these in the deck.
P(Diamond ∪ 7) = P( Diamond ) + P( 7 ) - P( Diamond | 7)
= 13/52 + 4/52 - 1/52
= 16/52 = 4/13
5) Randomly selecting a red card or a queen.
There are 26 red cards in the deck, from diamonds and hearts suits, 13 from each. There are 4 queens in the deck, one from each suit. The joint event is a queen of a diamonds or hearts, which there are 2 of in the deck.
P( Red ∪ Queen ) = P( Red ) + P( Queen ) - P( Red | Queen)
= 26/52 + 4/52 - 2/52
= 28/52 = 7/13
6) Randomly selecting a three or a face card.
There are 4 threes in a deck of cards, one from each suit. There are 12 face cards in a deck (Jack, Queen, and King with three from each suit). There is no joint event because you cannot draw a three and a face card. So this time we subtract 0 because the events are mutually exclusive.
P( 3 | Face ) = P( 3 ) + P( Face ) - P( 3 | Face )
= 4/52 + 12/52 - 0/52
= 16/52 = 4/13