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babydani11
19.10.2019 •
Mathematics
From a srandard deck of 52 cards, what is the probability of drawing two five cards with replacement?
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Ответ:
There are 4 ways that event A could occur: drawing a '5' of hearts, 5 of spades, 5 of diamonds, or five of clubs.
This is out of 52 cards total
For one card,
P(A) = 4/52 = 1/13
For two cards,
P(A and A) = P(A)*P(A)
P(A and A) = (1/13)*(1/13)
P(A and A) = 1/169
We're able to multiply like this because the events are independent (replacement occurs).
The answer as a fraction is 1/169
The answer in decimal form is approximately 0.005917
The answer as a percent is approximately 0.5917%
Ответ:
Since we want to solve for the variable x, we want to isolate x
a²x + (a - 1) = (a + 1)x ⇒ Distribute x to (a+1). Also, remove parentheses
a²x + a - 1 = ax + x ⇒ Subtract a from both sides
a²x - 1 = ax + x - a ⇒ Add 1 to both sides
a²x = ax + x - a + 1 ⇒ Subtract (ax + x) from both sides
a²x - (ax + x)= ax + x - a + 1 - (ax+x) ⇒ Simplify. Remember that multiplying positive by negative = negative
a²x - ax - x = ax + x - a + 1 - ax - x ⇒ Simplify
a²x - ax - x = -a + 1 ⇒ Factor out the x from a²x - ax - x
x(a² - a - 1) = -a + 1 ⇒ Divide both sides by (a² - a - 1)
x = (-a + 1) / (a² - a - 1)
However, we need to make sure that the denominator does not equal 0. Therefore, you set the denominator = 0 (just use the quadratic formula for this), and it gives that the denominator =0 when a = (1+√5)/2 AND (1-√5)/2
Therefore, the final answer is
x = (-a + 1) / (a² - a - 1) given that a ≠ (1+√5)/2, a ≠ (1-√5)/2