Anonymous
Anonymous asked in Science & MathematicsMathematics · 1 month ago

# Finding the probability of P((A ∪ B) ∪ C)?

Consider the random experiment in which one card is drawn from a standard deck of 52. Let RED be the event that a red card (hearts or diamonds) is drawn, BLACK be the event that a black card (clubs or spades) is drawn, EVEN means an even-numbered card is drawn (2, 4, 6, 8 or 10); ODD means an odd-numbered card is drawn (3, 5, 7 or 9 - aces not included); COURT means a court card (jack, queen, king or ace); TWO means a 2 of any suit is drawn, etc. Calculate the probability of:

(i) P((ODD ∪ BLACK) ∪ EVEN)

Relevance

There are 5 even cards in each of the 4 suits (20).

There are 4 odd cards in each of the 4 suits (16).

There are 26 black cards.

If we add that all up we get:

20 + 16 + 26 = 62

Clearly we've double-counted because there are 10 cards that are black & even and 8 cards that are black and odd.

Subtracting that we get:

62 - 18

= 44

This makes sense because the only cards that aren't included are the red court cards (4 cards × 2 red suits = 8). So another way to count it would be:

52 - 8

= 44

Dividing by the total number of cards, the probability is:

44/52

= 11/13

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