Grade 10 math (easy)

This might take me hours to do by myself and i have tonnes of other homework to do aswell, so any help is apreciated

Probability!!!!

1. A Card is cut form a normal 52 pack of cards. The suit is noted and the card is replaced, this process is twice repeated

A) Find the probability that all 3 cards are spades
B) Find the probability of getting at most 1 spade

2. A tetrahedal dice with faces numbered 1 - 4 is rolled. draw a simplified tree diagram to find the probability of getting the number 12

3) A stack of timber at the yard contains 10 lengths of each: 3.6, 3.5, 4.2, 4.5, 4.8 and 5.1 metre. The lengths are facing outwards, draw a simplified tree diagram and show the probability of pulling out 3 lengths greater then 4.5 by chance.

4.) whats the probability of tossing 5 heads in a row?

5) There are 20 bags of sugar on the shelf, and 4 bags break, so the sugar leaks. Use a simplified tree diagram to show the probability of getting 3 good bags, by chance.



Thanks! any help is appreciated

 

Question 1 A.

The probability of selecting a spade from a pack of 52 cards is 1/4. There are 4 suits, each comprising of 13 cards. 52/13 = 4, hence the probability is 1 in 4.

Now, in order to cut the first card as a spade, it would be a 1/4 chance, 25%
In order to cut the second card as a spade after placing the first card back into the deck would be 1/16.
In order to cut the third card as a spade after placing the second card back into the deck would be 1/64.

However, this is where it gets trick for some.

Actually selecting the card itself each time is merely a 25% chance, as each selection is an independent trial. However, if you are wanting to select 3 spades in a row, then the chance of that happening is 0.25 * 0.25 * 0.25 because the result is dependent.

The answer is 1/64 chance. Convert it however you wish.

Question 1 B.

I'm not sure how your teacher wants you to do this. I've done this in the assumption that you will only draw 3 cards.

In order to select at most one spade, a 3/4 chance must be satisfied across the bored, hence, the first, second, or third card need not be a spade, and therefore, the most probably way is a 3/4 chance throughout.

We then multiply.

3/4 * 3/4 * 3/4 = 27/64.

The chance of selecting only one spade, and two non-spades in three selections is 27/64. I'm fairly sure this is correct.

Quetsion 2.

This question doesn't make sense. If the die has 4 faces numbered 1 through to 4, then to roll the number 12 is impossible.

Question 3.

There are 60 lengths.

20 are greater than 4.5m.
40 are equal to, or less than 4.5m.

The chance therefore of pulling out a sheet of timber greater than 4.5m is 20/60, simplified to 1/3. In order to pull out 3 lengths greater than 20, then we must factor in a different equation everytime:

First pull 20/60.
Second pull 19/59.
Third pull 18/58.

We must factor this in, as for every pull, we are deducting 1 unit of timber from the data-set, and must compensate by subtracting 1 from the denominator, indicating the total number of units of timber, and subtracting 1 from the numerator, indicating the number of units of timber greater than 4.5m.

We multiply this together.

20/60 * 19/59 * 18/58 = 0.033313851548802.
Multiply this by 100 to convert to a percentage, and round to two decimal places.

3.33%.

That is the chance of pulling 3 units of timber with a length greater than 4.5m.

You do the tree diagram yourself.

Question 4.

This one is rather easy, and can be done in your head.

The probability of having a coin land on heads is 1/2. We simply multiply a half five times in order to figure out the dependent percentage for flipping five heads consecutively.

1/2 * 1/2 * 1/2 * 1/2 * 1/2 = 0.03125
Multiply by 100 to convert to a percentage.

3.125%.

There is a 3.125% chance to flip five heads in a row.

Question 5.

4/20 bags are considered bad. We simplify this to 1/5.

This means, the probability of selecting one good bag are 16/20. To pull 3, like question 3, we must account for change and multiply.

First pull, 16/20.
Second pull, 15/19.
Third pull, 14/18.

16/20 * 15/19 * 14/18 = 0.49122807017544
Multiply by 100, and round to two decimal places for a percentage.

49.12%.

The chance of pulling 3 good bags are 49.12%.

You do the tree diagram yourself.


TL;DR answers:

Question 1 A - The probability of pulling 3 spades in a row in a deck of 52 cards is 1/64.
Question 1 B - The probability of selecting at the very most one spade is 27/64.
Question 2 - This doesn't make sense.
Question 3 - The chance of pulling out 3 sheets of timber that have a length greater than 4.5m is 3.33%.
Question 4 - There is a 3.125% chance of tossing 5 heads in a row.
Question 5 - There is a 49.12% chance of pulling 3 good bags of sugar consecutively.


Hope that helped, you may want to check them yourselves, I did it in around 5 minutes, bar the typing.

 

Cool, answered, Lock this please.

 

Not even a thank you?

 

lolol agreed platypi

 

"Cool, answered?" Really? He did all of that work for you, and you write that? That's incredibly rude. Not even a thank you?

 

Ive had Malaka dang on Msn for a couple months now, after he answered this i spoke to him and got help with a few more questions and thanked him then,

Please stop spamming trying to get your post count up for stuff you dont know about,
I said "Cool answered" a week after he posted...