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VCE Stuff => VCE Mathematics => VCE Mathematics/Science/Technology => VCE Subjects + Help => VCE Mathematical Methods CAS => Topic started by: lacoste on January 09, 2009, 12:42:38 pm

Title: Probability
Post by: lacoste on January 09, 2009, 12:42:38 pm: Qst A).

A coin is tossed 3 times and you note that the coin lands heads exactly twice. What is the probability that the first toss was the tail?

Help please, any help appreciated
Title: Re: Probability
Post by: Flaming_Arrow on January 09, 2009, 12:53:03 pm: whats the answer?
Title: Re: Probability
Post by: lacoste on January 09, 2009, 01:00:53 pm: Quote from: Flaming_Arrow on January 09, 2009, 12:53:03 pm
whats the answer?
Qst. A)
1/3
Title: Re: Probability
Post by: lacoste on January 09, 2009, 01:04:26 pm: These questions are from Conditional and Multiplication Rule Probability.. Including Qst. A)
Im not sure how they got the answers.

Qst B) A pair of fair dice are rolled. Find the probability that both numbers are odd given that the first die shows a number less than 4?
Title: Re: Probability
Post by: Mao on January 09, 2009, 01:13:18 pm: A) I won't use maths, because the question is not too complicated:

exactly two H, meaning the possible combinations are: THH, HTH, HHT

hence the chance of T first is 1/3

B)

both odd = first odd * second odd

$Pr(first\; odd)=Pr(odd|<4)=\frac{2}{3}$

second odd is 1/2

hence both odd given that first is less than 4 would be 1/3
Title: Re: Probability
Post by: Flaming_Arrow on January 09, 2009, 01:14:22 pm: 1.
$1T|2H = \frac {1T \cap 2H}{2H}$

$\frac {0.5 \cdot 0.5 \cdot 0.5}{3C2 \cdot 0.5 \cdot 0.5 \cdot 0.5} = \frac {1}{3}$
Title: Re: Probability
Post by: lacoste on January 10, 2009, 03:28:20 pm: Quote from: Flaming_Arrow on January 09, 2009, 01:14:22 pm
1.
$1T|2H = \frac {1T \cap 2H}{2H}$

$\frac {0.5 \cdot 0.5 \cdot 0.5}{3C2 \cdot 0.5 \cdot 0.5 \cdot 0.5} = \frac {1}{3}$

Why is it 3C2?
Does that mean 3 Combination? / a coin is tossed 3 times.

Shouldn't it be 3(0.5 * 0.5), because its 2 heads(50/50 chance) and three tosses?
Title: Re: Probability
Post by: Flaming_Arrow on January 10, 2009, 05:42:28 pm: Quote from: lacoste on January 10, 2009, 03:28:20 pm
Quote from: Flaming_Arrow on January 09, 2009, 01:14:22 pm
1.
$1T|2H = \frac {1T \cap 2H}{2H}$

$\frac {0.5 \cdot 0.5 \cdot 0.5}{3C2 \cdot 0.5 \cdot 0.5 \cdot 0.5} = \frac {1}{3}$

Why is it 3C2?
Does that mean 3 Combination? / a coin is tossed 3 times.

Shouldn't it be 3(0.5 * 0.5), because its 2 heads(50/50 chance) and three tosses?
3C2 as in 2 heads in 3 tosses
Title: Re: Probability
Post by: lacoste on January 10, 2009, 05:47:52 pm: what does that equate to?

so 3C2 is equal to just 3?

why havnt i heard of"3C2" notation is that part of permuations or sumthin
Title: Re: Probability
Post by: Flaming_Arrow on January 10, 2009, 05:50:15 pm: its nCr

$3C2 = \frac {3 \cdot 2\cdot 1}{2 \cdot 1} = 3$