12 of 57 Items .... Course: PROBABILTY

A quick probability question ...

Player A's score is determined by taking the highest of 3 dice.
Player B's is determined by taking second-highest of 8.
Who wins more games?

.: [PROBABILTY], [Ben Orlin], [Number Theory].

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Mr Smith has two children. One of them is a boy. What is the probability the other child is also a boy?

.: [PROBABILTY], [SolveMyMaths], [Puzzle].

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Skimming the MTBoS Finds Interesting Things video from the Global Math department.

Which will be more likely to occur first
in a string of coin tosses, HTH or HTT?

This is the kind of question that becomes difficult because of assumptions made by the listener, assumptions that change the problem subtly and thus change the resulting expected probability.

The listener/reader here naturally changes this question to "Which group of three is more likely?", but that is not what he asked. We should refer back to the Monty Hall question.

.: [PROBABILTY], [Bob Lochel], [Strategy].

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Would you guess? $250,000 if correct and $100,000 if she refuses to try for it.

.: [PROBABILTY], [Curmudgeon], [Which Would You Choose?].

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If the average golfer is able to get a hole-in-one once in approximately 3000 rounds of golf (18 holes apiece), then what is the probability of any one of 100 average golfers getting a hole-in-one on the 5th hole during the weekend golf tournament?

What's the best way to find this out if you're the insurance company that will write this policy?

.: [PROBABILTY], [T.R.Milne], [The RealWorld].

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Consider eight objects. We will choose them one at a time, two at a time, three at a time, and so on.

Which of these will result in identical numbers of ways?
Why?

.: [PROBABILTY], [T.R.Milne], [Combinatorics].

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The cast of a school play that requires 4 girls and 3 boys is to be selected from 7 eligible girls and 9 eligible boys.

Will it be a different calculation if the boys are willing to play girls' parts, as in Shakespeare's time? If so, how will it be different?

.: [PROBABILTY], [T.R.Milne], [Combinatorics].

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Sullivan bought a die at the magic shop. He
rolls it 155 times and gets the following results:

ONE: twenty-eight times

TWO: twenty times

THREE: fifteen times

FOUR: thirty-one times

FIVE: thirty-two times

SIX: twenty-nine times.

Is this die loaded?

What is the probability he will get a 6 on the next roll?

.: [PROBABILTY], [T.R.Milne], [Number Theory].

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Once upon a time, the world's smartest person (Marilyn vos Savant, IQ: 228) received a question for her newspaper column.

Suppose you're on a game show, and you're given the choice of three doors. Behind one door is a car, behind the others, goats. You pick a door, say number 1, and the host, who knows what's behind the doors, opens another door, say number 3, which has a goat. He says to you, "Do you want to pick door number 2?"

Is it to your advantage to switch your choice of doors?
Craig. F. Whitaker, Columbia, MD

Marilyn's answer was surprising to many people. What do you think?

.: [PROBABILTY], [internet], [Explainer].

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Which would you press ... and why?

.: [PROBABILTY], [internet], [Which Would You Choose?].

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5 distinct numbers are chosen at random from {1,2,3,4,5,6,7,8,9}.

p(k) = probability their sum = k.

What are some of the ways you can find this in general?
What sum is/are the least likely?
Which sum is/are most likely?

p(15)=?

p(35)=?

.: [PROBABILTY], [James Tanton], [Raw Pure Math].

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Which lock is more secure?

1.

2.

3. (three numbers needed)

.: [PROBABILTY], [T.R.Milne], [Comparisons].