When a fair die is thrown, what is the probability of getting: The number 6 A nu

Question

When a fair die is thrown, what is the probability of getting: The number 6 A number that is a multiple of 2 A number that is greater than 5 A number that is less than 7 An even number Consider a deck of 52 cards with Face cards Jacks, Queens, and Kings (cards with pictures of their names). What is the probability of the following: A face card is drawn A red card or a card showing a 5 A card that is not a 5 or a Queen or a 7 A card that is a red face card. A card that is not a face card Now recalculate a. through e. but with a deck of cards that includes an additional suit. So the deck would include, Hearts, Diamonds, Clubs, Spades and Circles Define: population sample parameter statistic

Explanation / Answer

Solution:-

5) A = The number 6 - {6}

P(A) = 1/6
6) A = A number that is a multiple of 2 - {2,4,6}
P(A) = 3/6 = 1/6
7) A = Number greater than 5 - {6}
P(A) = 1/6
8) A = Number less than 7 - {1,2,3,4,5,6}
P(A) = 6/6 = 1
9) A = An even number - {2,4,6}
P(A) = 3/6 = 1/2
10) A = A face card is drawn
There are 12 face cards in a deck, these are 4 Jack, 4 King, 4 Queen
P(A) = 12/52 = 3/13
11) A = A red card or a card showing 5
There are 26 red cards in total and 4 cards with number 5, however two of them are red. So, in total 28 cards we can choose out of 52.
P(A) = 28/52 = 7/13
12) A = A card that is not a 5 or a Queen or a 7
There are 4 cards with number 5, 4 cards with Queen, 4 cards with number 7.
So, we are not considering these 12 cards, out of 52, we can choose 40 cards.
P(A) = 40/52 = 10/13
13) A = A red face card.
6 of the face cards are red (diamonds or hearts) and 6 of the face cards are black (spaces or clubs).
P(A) = 6/52 = 3/26
14) A = A card that is not a face card.
P(A) = 40/52 = 7/13
15) Deck includes Hearts, Diamonds, Clubs, Spades and Circles.
Now we have in total 65 cards.
(a) A = A face card is drawn
There are 15 face cards in a deck, these are 5 Jack, 5 King, 5 Queen
P(A) = 16/65
(b) A = A red card or a card showing 5.
If the Circles are black then the answer is -
There are 26 red cards in total and 5 cards with number 5, however two of them are red. So, in total 29 cards we can choose out of 52.
P(A) = 29/65
If Circles are red, then -
There are 39 red cards in total and 5 cards with number 5, however three of them are red. So, in total 41 cards we can choose out of 52.
P(A) = 41/65
(c) A = A card that is not a 5 or a Queen or a 7
There are 5 cards with number 5, 5 cards with Queen, 5 cards with number 7.
So, we are not considering these 15 cards, out of 65, we can choose 50 cards.
P(A) = 50/65
(d) A = A red face card.
If Circles are not red, then
6 of the face cards are red (diamonds or hearts)
P(A) = 6/52 = 3/26
If Circles are red, then
9 of the face cards are red, then
P(A) = 9/65
(e) A = A card that is not a face card.
P(A) = 40/65

17) Population - Population is the entire pool from which a statistical sample is drawn.
18) Sample - In statistics, a sample refers to a set of observations drawn from a population.
19) Parameter - A parameter is a measurable characteristic of a population, such as a mean or a standard deviation.
20) Statistic - A statistic is a characteristic of a sample. Generally, a statistic is used to estimate the value of a population parameter.

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