math help needed

[BodybldgDoc]

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1. If an ordinary coin is tosses six times, what is the probability of either all heads or all tails?
A 1/4
B 1/32
C 1/3
D 1/8
E 1/16

Answer= B But how?

2. The angles of a triangle are in the ratio of 2:3:5. what is the measure of the smallest angle?
A 48
B 36
C 45
D 72
E 60
Answer= C ?

3. Julie has $5.50 in nickels and dimes. She has 5 more nickels than dimes. How many dimes does she have?
A 30
B 25
C 20
D 35
E 40
Answer=D pls explain

 

[Ex_EE]

1. After the first toss you have 5 tosses that need to match the first so each time your chance is 1/2. All you have to do is
1/2 * 1/2 * 1/2 * 1/2 *1/2 = (1/2)^5 = 1/32

2. I think the answer is wrong. The angles of a triangle add up to 180. So,
2x + 3x + 5x = 180
10 x = 180
x = 18
smallest angle is 2x = 36

3. 5.5 = .1(D) + .05(N)
N = D+5 (5 more nickles than dimes)
5.5 = .1d +.05D + .25
5.25 = .15D
D = 5.25/.15 = 35

 

[ananda]

1. Probability of all heads in 6 tosses:
(1/2)^ 6 = 1/64
Probability of all tails in 6 tosses:
(1/2)^6 = 1/64

Probability of all heads or all tails:
1/64 + 1/64 = 2/64 = 1/32


Guys correct me if I'm wrong, but this is how I would do it.

 

[Streetwolf]

They both work. Here's the step Ex_EE didn't explicitly type:

First coin can be heads or tails so the probability of flipping heads or tails is 1/2 + 1/2 = 1.

So p(coin 1 head or tail) = 1

The rest was written correctly:

Each subsequent coin flip must remain that particular side. There is (5 choose 5) or 1 way to do this: those 5 flips are the same. So we only need the probabilities, which are all 1/2.

First coin: 1
Second coin: 1/2
Third coin: 1/2
...
Sixth coin: 1/2

Multiply all together = 1/32


Ananda, that's probably how I'd have done it too. You just separated the first coin's probability. Since the above uses an 'or' relationship, it just adds together the 1/2 and 1/2 that you put in your calculations. Rather than do (1/2)^6 + (1/2)^6, Ex_EE pulled out (1/2)^5 to get (1/2)^5 * (1/2 + 1/2).

 

[BodybldgDoc]

great thx u guys