#1) Consider the experiment of rolling a single die. Find the probability of the event described.
What is P(odd and prime)?
A) 1/6
B) 1/2
C) 1/3
D) 2/3
#2) Consider the experiment of selecting a card from an ordinary deck of 52 playing cards and determine the probability of the stated event.
A black card or a seven is drawn.
A) 1/26
B) 2/13
C) 15/26
D) 7/13
#3) Each letter of the alphabet is written on a separate piece of paper and placed in a box. Find the probability of drawing a vowel, {a, e, i, o, u}, or a letter in the word "Segments"
A) 5/13
B) 6/13
C) 11/26
C) 1/2
#1) To find the probability of the event "odd and prime" when rolling a single die, we need to determine the number of outcomes that satisfy both conditions and divide it by the total number of possible outcomes.
First, let's identify the odd numbers on a die: 1, 3, and 5.
Next, we check which of these numbers are prime. Prime numbers are numbers greater than 1 that cannot be divided evenly by any other number besides 1 and itself. In this case, only the number 3 is prime.
So, the favorable outcome is rolling a 3, and there is only one favorable outcome.
The total number of possible outcomes when rolling a single die is 6 (since a die has 6 sides, numbered from 1 to 6).
Therefore, the probability of rolling an odd and prime number is 1/6.
So, the answer is A) 1/6.
#2) To find the probability of drawing a black card or a seven from an ordinary deck of 52 playing cards, we need to determine the number of favorable outcomes and divide it by the total number of possible outcomes.
First, let's count the total number of black cards in a deck. There are 26 black cards (clubs and spades) in a deck.
Next, let's count the number of sevens in a deck. There are four sevens (one in each suit: clubs, diamonds, hearts, and spades).
However, we need to make sure we don't count the seven of spades twice since it is both black and a seven. Therefore, we subtract one from the total count of black cards.
The number of favorable outcomes is 26 + 4 - 1 = 29.
The total number of possible outcomes when drawing a card from a deck is 52 (since there are 52 cards in a deck).
Therefore, the probability of drawing a black card or a seven is 29/52.
So, the answer is C) 15/26.
#3) To find the probability of drawing a vowel (a, e, i, o, u) or a letter in the word "Segments" from a box containing all the letters of the alphabet, we need to determine the number of favorable outcomes and divide it by the total number of possible outcomes.
Firstly, let's count the total number of letters in the word "Segments." There are seven letters in total: S, e, g, m, n, t, and s.
Next, we need to count the total number of vowels in the alphabet. There are five vowels: a, e, i, o, and u.
Since the task requires us to draw either a vowel or a letter in the word "Segments," we need to make sure we don't count any duplicates.
The number of favorable outcomes is 7 + 5 - 1 = 11 (since there is one common letter, "s," between "Segments" and the vowels).
The total number of possible outcomes is 26 (since there are 26 letters in the alphabet).
Therefore, the probability of drawing a vowel or a letter in the word "Segments" is 11/26.
So, the answer is C) 11/26.