Math Is Fun Forum

bob's

Member

Registered: 2007-05-31

Posts: 5

can someone check+ stats!

1) A Market survey is conducted to determine whether a sports store should carry expensive training equipment for skiers.
The propositions of people who participate in skiing, skating, and racquet sports are as follows:
Skiing: 0.40
Skating: 0.55
Racquet sports: 0.35
Skiing and Skating: 0.05
Skiing and Racquet sports: 0.15
Skating: and Racquet sports: 0.15
All of the 3: 0.05
What is the probability that a person chosen at random would only participate in skiing?
My answer:

Probability= # of favourable outcome / total possible outcomes
0.40 + 0.55+0.35 +0.05 +0.15+0.15 +0.05 = 1.70
Skiing= 0.40
So:
Probability= # of favourable outcome / total possible outcomes
= 0.40/ 1.70
= .2352941176 --> 24%

2) To play a game, a die is rolled to see who plays first. Four players are going to play the game. What is the probability that at least two people roll the same number?

My answer:
12P2 = 132
24P2 = 552
Probability is 132/552 = 0.2391304348 --> 24%

Thanks in advance

Stanley_Marsh

Member

Registered: 2006-12-13

Posts: 345

Re: can someone check+ stats!

I got the same answer as you did on the first one

the second one , however   I got 13/18
Four player throw dices, the result can be listed

_ _ _ _  (each blank can be filled in with 1,2,3,4,5,6)
Let's consider the counter situation
the first blank can take value from 1 to 6 , ( choose 1 from 6)
Since the second blank must be different ,there only 5 choice ( choose 1 from 5)
So on...
and the number of arrangement that four players roll different number  is  6x5x4x3
the probability of four players roll different number will be  (6x5x4x3)/(6x6x6x6)
then , at least two ppl roll the same number will be  1- (6x5x4x3)/(6x6x6x6)

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Numbers are the essence of the Universe

mathsyperson

Moderator

Registered: 2005-06-22

Posts: 4,900

Re: can someone check+ stats!

The answer to the first one is a bit more complicated. It's a Venn Diagram-style question.

First we need to work out what proportion of people do only skiing and skating.
0.05 do those, and 0.05 do all three, so the proportion that do only those is 0.

By similar reasoning, we can work out that 0.1 of the people do only skiing and racquet sports, and that 0.1 of the people do only skating and racquet sports.
From there, we can work out how many people do only skiing.

The total amount of skaters is given by the amount of people that only ski, and the amount that only skate and ski, and the amount that only ski and racquet, and the amount that do all three.
We know these last three amounts, so we can work out the first one.

Pure skiers = 0.4 - 0.1 - 0 - 0.05 = 0.25 --> 25%.

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Why did the vector cross the road?
It wanted to be normal.

Stanley_Marsh

Member

Registered: 2006-12-13

Posts: 345

Re: can someone check+ stats!

Skiing: 0.40
Skating: 0.55
Racquet sports: 0.35
These are not pure Skiing , skating and Racquet? OH , Nevermind.then,

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Numbers are the essence of the Universe