Suppose that 5 cards are drawn from a well-shuffled deck of 52 cards. What is the probability that all 5 are not black?

1 answer:

6 0

Here's the way I see it: 5 cards are drawn, one by one, without replacement. Half (or 26) of the original deck are black and half (26) are white.

P(5 are not black) = P(5 are red)

P(5 are not black) = P(first card is red) * P(second card is red) * P(third card is red)*P(fourth card is red)*P(fifth card is red) =

(26/52) * (25/51) * (24/50) * (23/49) * (22/48) = 0.025 (answer)

We start with 52 cards. We draw one, leaving 51 cards, 25 of which are red. And so on.

You might be interested in

At 2 PM, a thermometer reading 80°F is taken outside where the air temperature is 20°F. At 2:03 PM, the temperature reading yiel

Alexeev081 [22]

Use Law of Cooling:
$T(t) = (T_0 - T_A)e^{-kt} +T_A$
T0 = initial temperature, TA = ambient or final temperature

First solve for k using given info, T(3) = 42
$42 = (80-20)e^{-3k} +20 \\ \\ e^{-3k} = \frac{22}{60}=\frac{11}{30} \\ \\ k = -\frac{1}{3} ln (\frac{11}{30})$

Substituting k back into cooling equation gives:
$T(t) = 60(\frac{11}{30})^{t/3} + 20$

At some time "t", it is brought back inside at temperature "x".
We know that temperature goes back up to 71 at 2:10 so the time it is inside is 10-t, where t is time that it had been outside.
The new cooling equation for when its back inside is:
$T(t) = (x-80)(\frac{11}{30})^{t/3} + 80 \\ \\ 71 = (x-80)(\frac{11}{30})^{\frac{10-t}{3}} + 80$
Solve for x:
$x = -9(\frac{11}{30})^{\frac{t-10}{3}} + 80$
Sub back into original cooling equation, x = T(t)
$-9(\frac{11}{30})^{\frac{t-10}{3}} + 80 = 60 (\frac{11}{30})^{t/3} +20$
Solve for t:
$60 (\frac{11}{30})^{t/3} +9(\frac{11}{30})^{\frac{-10}{3}}(\frac{11}{30})^{t/3} = 60 \\ \\ (\frac{11}{30})^{t/3} = \frac{60}{60+9(\frac{11}{30})^{\frac{-10}{3}}} \\ \\ \\ t = 3(\frac{ln(\frac{60}{60+9(\frac{11}{30})^{\frac{-10}{3}}})}{ln (\frac{11}{30})}) \\ \\ \\ t = 4.959$

This means the exact time it was brought indoors was about 2.5 seconds before 2:05 PM

8 0

3 years ago

HELP ASAP WILL MARK BRAINLIEST<br> IF YOU DONT KNOW DONT ANSWER

NemiM [27]

Answer:

c is 120 degrees

3 0

2 years ago

Read 2 more answers

Express each ratio as a fraction in lowest terms.

uranmaximum [27]

1. 5/6
2. 7/1
3. 1/7
Just write the first number as the numerator and the second one as a denominator then divide by their common factors

6 0

3 years ago

What is the end behavior of the graph?

hichkok12 [17]

Imagine that this curve is a roller coaster. A dot on the roller coaster would be a car for a person to sit in, so to speak. As this car moves to the right, the car ultimately moves downward. So this means that as x gets larger, y gets smaller. Put another way: as x approaches infinity, f(x) approaches negative infinity.

Similarly, we can move the other way to work our way to the left. Moving to the left has us go up this time. As x approaches negative infinity, f(x) approaches positive infinity

These two facts point to choice B as the final answer

8 0

3 years ago

What is 0.04 divided by 23.6

Tcecarenko [31]

The answer is 0.0017. Do you not have a calculator?

5 0

3 years ago

Read 2 more answers