Probability

Which of the following are mutually exclusive events when a card is chosen at random from a standard deck of 52 cards?

• Choosing a 9 or a diamond

• Choosing an ace or a red card

• Choosing a king or a queen

• All of the above

Which of the following are mutually exclusive events when a fair die is rolled?

• Getting a number less than 3 or a multiple of 3

• Getting a factor of 4 or a number divisible by 2

• Getting an odd number or a factor of 3

• Getting a 2 or a prime number

All the following events are not mutually exclusive events EXCEPT:

• Drawing a jack or a heart from a standard deck of cards

• Choosing a factor of 6 or a multiple of 4 from the numbers 1-10

• Spinning a 1 or an odd number in a spinner with 4 congruent sectors

• Rolling a composite number or an event number in rolling a fair die

If P(A) = 0.25, and P(B) = 0.60, and P(A ∩ B) = 0.15 then,

• P(A ∪ B) = 0.80

• P(A ∪ B) cannot be determined

• events A and B are mutually exclusive

• events A and B are not mutually exclusive

Hermie rolled a fair die once. What is the probability that a 4 or a prime number will turn up?

A spinner is divided into 8 congruent sectors and numbered from 1 to 8. If it will be spun once, find the probability that it stops at a factor of 6 or a multiple of 3.

Each of the numbers 1 – 25 is written on a slip of paper, rolled, and put in a box and mixed thoroughly. If a slip of paper is picked at random, what is the probability that the number in it is even or a multiple of 4?

The probabilities of three employees Lara, Mary and Joseph to be promoted are 3/8 , 2/5 and 1/7 , respectively. Assume that only one employee will be promoted.

What is the probability that either Lara or Joseph will be promoted?

The probabilities of three employees Lara, Mary and Joseph to be promoted are 3/8 , 2/5 and 1/7 , respectively. Assume that only one employee will be promoted.

What is the probability that neither Lara nor Mary will be promoted?

There are 9 class officers composed of 5 males and 4 females. A group of 3 officers is to be selected at random to represent their class in a forum. What is the probability that the group will have at least 2 males?