Use the complement of the event to find the probability. A) You roll a 6-sided n
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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 2-9Explanation / Answer
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.
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