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1234Reasoning

Exercises

Exercise 1

An opaque box contains 10 colored marbles, 7 green ones and 3 yellow ones. The green marbles are numbered 1 through 7, the yellow ones 1 through 3. You shake the box and without looking you take out one marble.

a

What is the probability that the marble is yellow?

b

What is the probability that the marble has number 1 printed on it?

c

What is the probability that the marble has number 4 printed on it?

d

What is the probability that the marble is green with a number greater than 3 printed on it?

Exercise 2

A lottery is held. The lottery tickets have numbers 000 through 999. All tickets have been sold. A number is drawn completely randomly. That number will get second prize.

a

You have ticket number 113. What is the probability you win that prize?

b

Your friend tells you that she has a ticket with an even number. What is the probability that she wins second prize?

c

What is the probability that an even number is drawn?

d

Why are the probabilities at b and c different?

Ticket number 771 draws second prize. Next the number for first prize is drawn. Number 771 does not compete any more.

e

What is the probability of first prize for you now?

f

What is the probability of an even number now?

Exercise 3

You are throwing two dice and count the number of pips that come up on top.

a

What is the probability that 7 pips come up on top?

b

What is the probability of at most 7 pips?

c

What is the probability of more than 11 pips?

d

What is the probability of an even number of pips?

Exercise 4

During a soccer tournament a coin is tossed at the start of each match to determine which team gets the kick off. In this tournament Cambuur plays four matches.

a

What is the probability that Cambuur wins the toss in the first match and gets to kick off?

b

What is the probability that Cambuur gets to kick off all four matches?

c

What is the probability that Cambuur can kick off at least three times?

Exercise 5

You are tossing three coins.
Determine the probability of two times "tails".

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