Spinner Pair
Posted on | March 8, 2009 | Comments Off
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Spinner Pair
probability?
1-two coins are tossed simultaneously. what is the probability of tossing two heads?
2-a coin is tossed three times. what is the probability of tossing three heads in succession?
3-a coin is tossed three times. what is the probability of tossing exactly two heads?
4-a coin is tossed three times. what is the probability of tossing at least two heads?
5-a standard die is rolled. what is the probability of rolling a 4?
6-two standard dice are rolled. what is the probability of rolling a pair (both the same number)?
7-two standard dice are rolled. what is the probability of rolling a total of 9?
8-two standard dice are rolled. what is the probability that the total of the two dice is less than 6?
9-what is the probablitity of drawing a red face card from a standard deck of playing cards?
10-two identical spinners each have five equal sectors that are numbered 1 to 5. what is the probability of a total of 7 when you spin both spinners?
1) assuming a fair coin the probability of tossing one head is 0.5
the probability to tossing two heads in a row is:
0.5 * 0.5 = 0.25
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2, 3, 4)
Let X be the number of of heads tossed in three flips of a fair coin. X has the binomial distribution with n = 3 trials and success probability p = 0.5.
In general, if X has the binomial distribution with n trials and a success probability of p then
P[X = x] = n!/(x!(n-x)!) * p^x * (1-p)^(n-x)
for values of x = 0, 1, 2, ..., n
P[X = x] = 0 for any other value of x.
The probability mass function is derived by looking at the number of combination of x objects chosen from n objects and then a total of x success and n - x failures.
Or, to be more accurate, the binomial is the sum of n independent and identically distributed Bernoulli trials.
X ~ Binomial( n , p )
the mean of the binomial distribution is n * p = 1.5
the variance of the binomial distribution is n * p * (1 - p) = 0.75
the standard deviation is the square root of the variance = √ ( n * p * (1 - p)) = 0.8660254
The Probability Mass Function, PDF,
f(X) = P(X = x) is:
P( X = 0 ) = 0.125
P( X = 1 ) = 0.375
P( X = 2 ) = 0.375 ← Answer to 3
P( X = 3 ) = 0.125 ← Answer to 2
The Cumulative Distribution Function, CDF,
F(X) = P(X ≤ x) is:
x
∑ P(X = t) =
t = 0
P( X ≤ 0 ) = 0.125
P( X ≤ 1 ) = 0.5
P( X ≤ 2 ) = 0.875
P( X ≤ 3 ) = 1
1 - F(X) is:
n
∑ P(X = t) =
t = x
P( X ≥ 0 ) = 1
P( X ≥ 1 ) = 0.875
P( X ≥ 2 ) = 0.5 ← Answer to 4
P( X ≥ 3 ) = 0.125
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5)
one die is rolled. assuming the die is fair then the probability of rolling any of the six sides is 1/6.
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6)
Use this table to see all 36 outcomes of rolling two dice. The first column is the face showing on die1 and the first row is the face showing on die2. The other values in the table are the sum of the two dice.
___1___2___3___4___5___6
1__2___3___4___5___6___7
2__3___4___5___6___7___8
3__4___5___6___7___8___9
4__5___6___7___8___9___10
5__6___7___8___9___10__11
6__7___8___9___10__11__12
as you can see here, there are 6 ways to have pairs, 36 possible outcomes, you have a 1/6 probability of rolling pairs.
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7)
look at the table above, there are 4 ways to get a sum of 9, assuming fair die you have a probability of 4/36 = 1/9.
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P(sum less than six)
= P(sum = 2) + P(sum = 3) + P(sum = 4) + P(sum = 5)
= 1/36 + 2/36 + 3/36 + 4/36
= 10/36
= 5/18
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9)
there are six red face cards: Jack, Queen and King of Hearts and of Diamonds.
6/52 = 3/26
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10)
Look at the dice table without the column for rolling a six or the row for rolling a six.
___1___2___3___4___5
1__2___3___4___5___6
2__3___4___5___6___7
3__4___5___6___7___8
4__5___6___7___8___9
5__6___7___8___9___10
there a 4 ways to get a sum of 7, 25 possible outcomes
probability is 4/25.
misery business (spaige vs. sparcy)
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Mutually exlusive?
there is a Spinner divided into even 4 (circle divided into 4) each part is labeled 1,2,3,4 which of the following pairs of events are mutually exclusive?
(picture with the problem)
http://i34.photobucket.com/albums/d136/N4rumi/math1.jpg
P(2),P(even number)
P(3),P(prime number)
P(even number),p(odd number)
P(4),P(number greater than 2)
P(1),P(number less than3)
Mutually exclusive means they can't both happen.
case 1, 2 is also even, not that one
case 2, 3 is also prime, not that one
case 3, an even number can't also be odd, that's the one
case 4, 4 is also >2, not that one
case 5, 1 is also <3, not that one
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