Dice Game

 

 

The Most Common Last Digit of Multiplications

 

Source: Puzzle A Day

Worn Out Numbers

 

 

 

 

(taken from)

3 dice

source: PuzzleADayBlog

 

Leo the Rabbit

       source: Youcubed

Sum of Two Squares

You are going to be randomly assigned a number between 1 and 100 in a party game. For an activity, participants with a number card that is a total of two squares are called. (There are 100 participants)

What is the probability that you will be one of the participants?

12 Days of Christmas

If we choose three gifts randomly, what is the probability that they are all birds of the same kind?

Parallel Parking

 

Every weekend, I drive into town for contactless curbside pickup at a local restaurant. Across the street from the restaurant are six parking spots, lined up in a row.

While I can parallel park, it’s definitely not my preference. No parallel parking is required when the rearmost of the six spots is available or when there are two consecutive open spots. If there is a random arrangement of cars currently occupying four of the six spots, what’s the probability that I will have to parallel park?

Source:The Riddler

Three Die Together

Three die are randomly put together as shown above. 

What is the probability of the visible face totaling to 13?

In the example above the total is 3+4+5=12

 

Flag Colors

Problem 131: Quarter final combinations

Four English teams have progressed to the Champion's League quarter-finals. What is the probability of an all-English tie?















Hint 1
Hint 2
Hint 3

Problem 86: Bertrand's Box

Consider three boxes:

One of these boxes containing two gold coins; one contains two silver coins; the other contains one gold coin and one silver coin.

A box is chosen at random and one of the two coins inside is drawn. It turns out to be gold. What is the probability of the second coin in the box being gold?  

Source: Joseph Bertrand

Rich Tasks 40: Probability and Science

https://alportsyndrome.org/alport-syndrome/alport-syndrome-genetics/

1. What do you understand from the above image?

2. How is probability useful in determining whether a child will carry any of these traits?

https://www.newscientist.com/article/2191375-probability-helps-zebrafish-stay-in-schools-when-faced-with-predators/

3. What do you think of this news? Search about it and explain. Your answer should give necessary information about how probability is important in this situation.

Rich Tasks 38: Probability Grid

DOWNLOAD LINK
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Problem 52: Iceland's World Cup Adventure

http://www.goal.com/en-gb/news/russia-2018-iceland-becomes-smallest-nation-to-qualify-for-world-/1gwdmlxhdwsui1hzp4o0nu6rgz

Iceland participates to the Soccer World Cup for the first time in history. The people of this small island nation so excited.

They are going to play with Costa Rica, Argentina and Nigeria in the group stage.

Can you determine in how many different ways can they qualify to the second stage? This includes being in the top two positions. Points may vary for qualifying to the upper level. For example, consider all the games are draw. Then all teams will have 3 points each. Some other rules will be used to determine the teams which qualify.

Here are some other examples:

1. Argentina 9 points

2. Iceland 6 points

3. Nigeria 3 points

4. Costa Rica 0 points

1. Iceland 9 points

2. Costa Rica 7 points

3. Argentina 4 points

4. Nigeria 0 points

Problem 49: Mr. Oswald's phone

Mr. Oswald forgot the pass lock pattern on his mobile phone. He remembers that the pattern starts from the dot labeled A, and ends on the dot that is labeled B. The pattern is made by 4 strikes.

He decides to unlock his phone by trying some patterns. However after 5 wrong patterns the phone will be disabled for 5 minutes.

i.          How many different pattern can be drawn from A to B with 4 strikes?

ii.          What is the probability that he can unlock his phone without disabling it?

A pattern example is drawn on the phone image above.

Problem 46: Feet and Tails

Mrs. Eleanor Abernathy has 7 female cats. This May all her cats gave birth to new kittens. Some of the cats had 3 babies, some had 4 and the remaining ones had 5 baby cats. 

The number of cats that gave birth to 5 babies is 1 less than the number of cats that have quadruplets or triplets.

Mrs. Abernathy is interested in counting and she counts 150 legs in her house. 

Can you find the number of cats who has quints(5 babies)?

Problem 43: Alien Encounter

I saw this problem on another blog page. It is from Steven Strogatz's famous book Professor Stewart's Cabinet of Mathematical Curiosities. I like such Knights and Knaves type of logical reasoning questions. I use them a lot while teaching "Logic" in IB DP Math Studies course.

Here is the question:

 

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Solutions to such questions need seeing the big picture of the case, and often students struggle doing this. That's why I prefer them drawing diagrams or truth table-like charts. 

Sometimes a tree diagram from probability unit is helpful.
So let's try a solution using tree diagrams.

Assume that Alfy tells the truth. Therefore he must be a Veracitor. What he tells about Betty is also true. So Betty is Gibberish. Betty says Alfy and Gemma are same species but she is lying. Therefore Gemma must be Gibberish. This coincides with Gemma saying Betty is Veracitor, which she is not. So Gemma is a liar and it matches with what we found from Alfy and Betty's answers. So our answer is Alfy: Veracitor; Betty and Gemma: Gibberish.

It is better to see the other option where Alfy is dishonest. This time we see that, if he is a liar, then Betty must be a Veracitor. If Betty is Veracitor, then Gemma must be Gibberish since Betty is honest in this option. However being a Gibberish, Gemma must be a liar. However, Gemma says Betty to be a Veracitor which is true. This truth creates a contradiction. Therefore this option is not reasonable at all and Alfy must be telling the truth. So the answer is the previous one.

Problem 32: Taking Turns to Toss a Die

from: Cut the Knot

Math Pics 3: Perceptions of Probability and Numbers

Source