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3 years ago

8

two cards are drawn without replacement from a standard deck of 52 playing cards. find the probability that both are odd numbers

(aces are considered odd because they have a value of 1 or 11).

1 answer:

Ne4ueva [31]3 years ago

3 0

Odd cards: Ace, 3, 5, 7 , 9 , Jack, King
7 odd cards per suit, 4 suits = 7 * 4 = 28 odd cards
so 1st card being odd is a 28/52 = 7/13 probability

2nd card would be a 27/51 = 9/17 probability

7/13 x 9/17 = 63/221 probability of both

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3. What is the surface area of the triangular prism shown below?

jekas [21]

Answer:

1233cm^2

Step-by-step explanation:

a of triangle = 1/2 bh

1/2 x 12 x 9 = 54

108 x 2 = 108

a of regtangle = l x w

25 x 15 = 375

375 x 3 = 1125

total surface area = 1125 + 108 = 1233cm^2

7 0

2 years ago

The probability that your call to a service line is answered in less than 30 seconds is 0.75. Assume that your calls are indepen

vfiekz [6]

Answer:

a) 0.2581

b) 0.4148

c) 17

Step-by-step explanation:

For each call, there are only two possible outcomes. Either they are answered in less than 30 seconds. Or they are not. The probabilities for each call are independent. So we use the binomial probability distribution to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

In which $C_{n,x}$ is the number of different combinations of x objects from a set of n elements, given by the following formula.

$C_{n,x} = \frac{n!}{x!(n-x)!}$

And p is the probability of X happening.

In this problem we have that:

$p = 0.75$

a. If you call 12 times, what is the probability that exactly 9 of your calls are answered within 30 seconds? Round your answer to four decimal places (e.g. 98.7654).

This is $P(X = 9)$ when $n = 12$ . So

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$P(X = 9) = C_{12,9}.(0.75)^{9}.(0.25)^{3} = 0.2581$

b. If you call 20 times, what is the probability that at least 16 calls are answered in less than 30 seconds? Round your answer to four decimal places (e.g. 98.7654).

This is $P(X \geq 16)$ when $n = 20$

So

$P(X \geq 16) = P(X = 16) + P(X = 17) + P(X = 18) + P(X = 19) + P(X = 20)$

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$P(X = 16) = C_{20,16}.(0.75)^{16}.(0.25)^{4} = 0.1897$

$P(X = 17) = C_{20,17}.(0.75)^{17}.(0.25)^{3} = 0.1339$

$P(X = 18) = C_{20,18}.(0.75)^{18}.(0.25)^{2} = 0.0669$

$P(X = 19) = C_{20,19}.(0.75)^{19}.(0.25)^{1} = 0.0211$

$P(X = 20) = C_{20,20}.(0.75)^{20}.(0.25)^{0} = 0.0032$

So

$P(X \geq 16) = P(X = 16) + P(X = 17) + P(X = 18) + P(X = 19) + P(X = 20) = 0.1897 + 0.1339 + 0.0669 + 0.0211 + 0.0032 = 0.4148$

c. If you call 22 times, what is the mean number of calls that are answered in less than 30 seconds? Round your answer to the nearest integer.

The expected value of the binomial distribution is:

$E(X) = np$

In this question, we have $n = 22$

So

$E(X) = 22*0.75 = 16.5$

The closest integer to 16.5 is 17.

7 0

3 years ago

6th grade math, help pleasee:)

Debora [2.8K]

Answer:

1/5 cup

Step-by-step explanation:

Sugar: water

1 5

We want 1 cup water, so divide each side by 5

1/5 : 5/5

1/5 : 1

There is 1/5 cup sugar to 1 cup water

4 0

3 years ago

Read 2 more answers

Can some one help on 30? thx

MariettaO [177]

The lowest common multiple of 2 and 7 is 14, so 14 days will pass before he does both chores again.

5 0

3 years ago

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Find the value of n .<br> 6/n = 24/28<br> y = ___.

il63 [147K]

Answer:

$n=7$

Step-by-step explanation:

Cross multiply, isolate the variable, and divide by the coefficient to solve.

$\frac{6}{n}=\frac{24}{28} \\ \\ 24n=168 \\ \\ n=7$

Plug back in to check.

$\frac{6}{7}=0.857142857 \\ \\ \frac{24}{28} =0.857142857$

5 0

3 years ago