Use the complement of the event to find the probability A Yo

Use the complement of the event to find the probability. A) You roll a 6-sided number cube. What is the probability that you do not roll a 3? B) You roll a 6-sided number cube. What is the probability that you do not roll a multiple of 2? C) A) You roll a 6-sided number cube. What is the probability that you do not roll a prime D) You choose a card at random from a standard deck of cards. What is the probability that you do not choose a black queen? E) You choose a card at random from a standard deck of cards. What is the probability that you do not choose an ace? A bag contains 26 tiles, each with a different letter of the alphabet written on it. You choose a tile without looking. What is the probability that you choose a vowel (a, e, i, o, or u) or a letter in the word MATHEMATICS? A number icosahedron has 20 sides numbered 1 through 20. A) What is the probability that the result of a roll is a number less than 6 or greater than 17? B) What is the probability that the result of a roll is a multiple of 2 or a prime number? You are going to draw one card at random from a standard deck of cards. A standard deck of cards has 13 cards (2, 3, 4, 5, 6, 7, 8, 9, 10, jack, queen, king, ace) in each of 4 suits (hearts, clubs, diamonds, spades). The hearts and diamonds cards are red. The clubs and spades cards are black. Which of the following have a probability of less than 1/4? Choose all that apply. a. Drawing a card that is a spade and an ace b. Drawing a card that is a club or an ace c. Drawing a card that is a face card or a club d. Drawing a card that is black and a heart e. Drawing a red card and a number card from 2-9

Solution

For any event that can occur with a chance A(P(A)), there will be a chance that the event may not occur, given by A\', known as the complement of A.

The rule is that P(A) + P(A\') = 1, Therefore P(A\') = 1 - P(A)-------(1)

Also, the probability of an event happening P(A) = Number of Favourable Outcomes/Total No. of Outcomes.-----(2)

(53) What is the probability of not rolling a 3

(A) A six sided cube has the numbers 1,2,3,4,5 and 6. Let us find the probability of rolling a 3.

Here favourable outcomes = 1 (rolling a 3), while the total no. of outcomes = 6 (we can roll any of the 6 numbers)

Therefore P(rolling a 3) by equation (2) is = 1/6.

What we need is the complement of the event, that is probability of not rolling a 3.

By equation (1) P(not rolling a 3) = 1 - P(rolling a 3) = 1 - 1/6 = 5/6

(B) Probability of not rolling a multiple of 2.

The multiples of 2 are 2,4 and 6. Therefore the favourable outcomes = 3

Therefore P(rolling a multiple of 2) by equation (2) is = 3/6 = 1/2.

What we need is the complement of the event, that is probability of not rolling a multiple of 2.

By equation (1) P(not rolling a multiple of 2) = 1 - P(rolling a multiple of 2) = 1 - 1/2 = 1/2.

(C) Probability of not rolling a prime number.

The prime numbers are 2,3 and 5 (1, is not a prime number). Therefore the favourable outcomes = 3

Therefore P(rolling a prime number) by equation (2) is = 3/6 = 1/2.

What we need is the complement of the event, that is probability of not rolling a prime number.

By equation (1) P(not rolling a prime number) = 1 - P(rolling a prime number) = 1 - 1/2 = 1/2.

(D) While choosing a card, probability of not picking a black Queen.

Let us find the probability of picking a black queen. There are 2 black queens in a deck of 52 cards(Spades and Clubs).

Therefore the no. of favourable outcomes = 2 and the total no. of outcomes = 52

P(Picking a black Queen) = 2/52 = 1/26

We need the complement of this event: P(Not picking a black queen) = 1 - P(Picking a Black Queen)

= 1-1/26 = 25/26.

(E) While choosing a card, probability of not picking an Ace.

Let us find the probability of picking an Ace. There are 4 Aces in a deck of 52 cards.

Therefore the no. of favourable outcomes = 4 and the total no. of outcomes = 52

P(Picking an Ace) = 4/52 = 1/13

We need the complement of this event: P( Not picking an Ace) = 1 - P(Picking an Ace)

= 1-1/13 = 12/13.