Consider the experiment of selecting a card from an ordinary deck of 52 playing cards and determine the probability of a red card or a card showing a 5 is drawn.
I figured the red cards would be 26/52 and the 5 would be 4/52. Would I add these two together for the answer of 28/52 or do I keep these separated?
Your answers for the separate cases are correct. For the "either 5, red, or both" case, the probability is
[26 (any hearts or diamonds) + 2(5 of spades or clubs)]/52. That is NOT the sum of the probabilities of red or 5's.
To determine the probability of either drawing a red card or a card showing a 5 from a standard deck of 52 playing cards, you need to consider two separate events.
Event 1: Drawing a red card.
In a deck of 52 playing cards, half of them are red (26 cards are hearts or diamonds). Therefore, the probability of drawing a red card is 26/52.
Event 2: Drawing a card showing a 5.
There are four 5s in a deck of 52 cards (one in each suit: hearts, diamonds, clubs, and spades). Hence, the probability of drawing a 5 is 4/52.
Now, to determine the probability of either event occurring, you need to add the probabilities of the two individual events. Thus, the probability of drawing a red card OR a card showing a 5 is:
26/52 + 4/52 = 30/52
Simplifying this fraction by dividing both numerator and denominator by their greatest common divisor (2), you get:
15/26
In conclusion, the probability of drawing a red card OR a card showing a 5 from a standard deck of 52 playing cards is 15/26 or approximately 0.577.