a. There are four 5s that can be drawn, and $\binom43=4$ ways of drawing any three of them. There are $\binom{52}3=22,100$ ways of drawing any three cards from the deck. So the probability of drawing three 5s is

$\dfrac{\binom43}{\binom{52}3}=\dfrac4{22,100}=\dfrac1{5525}\approx0.00018$

In case you're asked about the probability of drawing a 3 or a 5 (and NOT three 5s), then there are 8 possible cards (four each of 3 and 5) that interest you, with a probability of $\frac8{52}=\frac2{13}\approx0.15$ of getting drawn.

b. Similar to the second case considered in part (a), there are now 12 cards of interest with a probability $\frac{12}{52}=\frac3{13}\approx0.23$ of being drawn.

c. There are four 6s in the deck, and thirteen diamonds, one of which is a 6. That makes 4 + 13 - 1 = 16 cards of interest (subtract 1 because the 6 of diamonds is being double counted by the 4 and 13), hence a probability of $\frac{16}{52}=\frac4{13}\approx0.31$ .

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Note: $\binom nk$ is the binomial coefficient,

$\dbinom nk=\dfrac{n!}{k!(n-k)!}={}_nC_k=C(n,k)=n\text{ choose }k$

6 0

3 years ago

Among 21- to 25-year-olds, 29% say they have driven while under the influence of alcohol. Suppose that three 21- to 25-year-olds

Sophie [7]

Answer:

P(3) = 0.0244

P(3) = 2.44%

the probability that all three selected have driven while under the influence of alcohol is 2.44% or 0.0244

Step-by-step explanation:

Given;

The probability that they have driven while under the influence of alcohol is;

P = 29% = 0.29

the probability that all three selected have driven while under the influence of alcohol is;

P(3) = P × P × P

P(3) = 0.29 × 0.29 × 0.29

P(3) = 0.024389

P(3) = 0.0244

P(3) = 2.44%

the probability that all three selected have driven while under the influence of alcohol is 2.44% or 0.0244

5 0

2 years ago

I need help with this question plzzz Geometry

KATRIN_1 [288]

Answer:

If the perimeter of a square measures 32 cm, each side measures 32/4= 8 cm, because all sides are equal.
The diagonal that passes through the center of the square divides the square into two triangles. The triangles are formed by a hypotenuse (the diagonal, which is k in this case), and two sides, that measure 8 cm each, in this case.
Because of Pythagoras' theorem, we know that the lenght of the hypotenuse (in this case the hypotenuse is k) equals the squared root of the sum of the squared sides, which in this case can be expressed as $k=\sqrt{8^2+8^2} =\sqrt{64+64}=\sqrt{128}=11.31$ .
Then, k=11.31 cm.

3 0

2 years ago

Part A: Identify the point that is an x-intercept in order from left to right (1st)

zvonat [6]

Answer:

Using a Graph of a Line Identify the x-axis. A coordinate graph has a y-axis and an x-axis. The x …

Using the Equation of the Line Determine that the equation of the line is in standard form. The …

Using the Quadratic Formula Determine that the equation of the line is a quadratic equation. A

Step-by-step explanation:

3 0

2 years ago