Final answer:
The odds of being dealt a four or a spade from a standard deck of cards are 1 in 13, which is option a). This is due to there being 16 favorable cards out of 52, simplified to 4 out of 13 after accounting for the four of spades.
Step-by-step explanation:
The question asks for the odds of being dealt a four or a spade in a standard deck of cards.
To solve this, we need to consider that a standard deck of 52 cards consists of four suits (hearts, spades, clubs, and diamonds), each with 13 cards, and the cards of each suit range from Ace through King, which includes the 'four' of each suit.
Firstly, there are four 'fours' in the deck, one in each suit. Since we want the odds of drawing a four of any suit, we have 4 chances out of 52. Similarly, there are 13 spades in the deck, giving us 13 chances out of 52 to draw a spade. However, we must consider that one of the spades is a four as well, which we have already counted. To avoid double-counting, we subtract this from the total.
The total number of favorable outcomes is therefore 4 (fours) + 13 (spades) - 1 (the four of spades already counted), which equals 16. Therefore, the odds are 16 chances out of 52. To simplify, divide both the numerator and the denominator by 4, which gives us 4 chances out of 13, so the correct answer is 1 in 13.
Since option a) 1 in 13 represents this simplified ratio, it is the correct option in the final answer.