1. A card is drawn from an ordinary deck of 52 playing cards. What are the odds in favor of drawing an ace?
2. The letters of the word mathematics are written on separate pieces of paper and put in a hat. What is the probability of drawing a vowel from the hat? (vowels are a, e, i, o, u) .
1.
4/52 = 1/13
2.
4/11
1. To find the odds in favor of drawing an ace, we need to determine the number of successful outcomes (drawing an ace) and the total number of possible outcomes (drawing any card).
First, let's determine the number of successful outcomes. In a standard deck of playing cards, there are 4 aces (one for each suit - hearts, diamonds, clubs, and spades). Therefore, the number of successful outcomes is 4.
Next, let's determine the total number of possible outcomes. A standard deck of playing cards contains 52 cards. Therefore, the total number of possible outcomes is 52.
To find the odds in favor of drawing an ace, we divide the number of successful outcomes by the total number of possible outcomes:
Odds in favor of drawing an ace = (Number of successful outcomes) / (Total number of possible outcomes)
= 4 / 52
= 1 / 13
So, the odds in favor of drawing an ace are 1 in 13.
2. To find the probability of drawing a vowel from the hat, we need to determine the number of successful outcomes (drawing a vowel) and the total number of possible outcomes (drawing any letter).
First, let's determine the number of successful outcomes. The word "mathematics" has 5 vowels (a, e, i, o, u). Therefore, the number of successful outcomes is 5.
Next, let's determine the total number of possible outcomes. The word "mathematics" has a total of 11 letters. Therefore, the total number of possible outcomes is 11.
To find the probability of drawing a vowel, we divide the number of successful outcomes by the total number of possible outcomes:
Probability of drawing a vowel = (Number of successful outcomes) / (Total number of possible outcomes)
= 5 / 11
So, the probability of drawing a vowel from the hat is 5/11.