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cluponka
2 months ago
5

In the game of blackjack played with one​ deck, a player is initially dealt 2 different cards from the 52 different cards in the

deck. a winning​ "blackjack" hand is won by getting 1 of the 4 aces and 1 of 16 other cards worth 10 points. the two cards can be in any order. find the probability of being dealt a blackjack hand. what approximate percentage of hands are winning blackjack​ hands?
Mathematics
1 answer:
tester [12.3K]2 months ago
6 0

The blackjack hand consists of:

One of the four aces: probability = 4 / 52

One of the sixteen cards valued at 10 points (10, jack, queen, king): probability = 16 / 52

Assuming cards are dealt sequentially without replacement,

The total probability of a blackjack hand is:

<span>P = (first card ace * second card 10-point) + (first card 10-point * second card ace)</span>

P = (4 / 52) * (16 / 51) + (16 / 52) * (4 / 51)

P = 0.04827, or approximately 4.83%

Therefore, the chance of receiving a blackjack hand is around 4.83%.

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According to a survey by Bankrate, of adults in the United States save nothing for retirement (CNBC website). Suppose that adult
tester [12383]

Complete Question

The complete question appears in the first uploaded image

Answer:

a) Yes, selecting 15 corresponds to a binomial experiment

b)

c)

d) P(r = 15) = 3.2768 *10^{-11}

Step-by-step explanation:

Regarding question a:

For an experiment to qualify as binomial

the trials have to be independent

each trial must yield one of two possible outcomes

Given that the selection of 15 individuals is random, we ascertain that the trials are independent and the outcomes are “either the individual saves for retirement or does not save for retirement.”

Therefore, we conclude that the selection of 15 people at random is indeed a binomial experiment.

In question b:

The probability that all selected adults do not save for retirement is mathematically modeled as

P(r = n) = ^nC_r * p^r * q^{n-r}

Here C signifies combination

r = 15 implies all selected adults

n refers to the population size equating to 15

From the problem, p = 0.20

and q can be calculated as

=>

=> q = 1 - p

Thus

P(r = 15) = ^{15}C_{15} * p^{15} * q^{15-15}

P(r = 15) = 3.2768 *10^{-11} Regarding question c:

The probability that exactly five of the selected adults do not save for retirement is mathematically modeled as

P(r = 5) = ^{15} C_5 * (0.20)^5 * (0.80)^{15}

P(r = 5) = 0.1032

In relation to question d:

The probability that at least one of the selected adults opts not to save for retirement can be mathematically expressed as

P(r \ge 1 ) = 1 - P (r = 0 )

P(r \ge 1 ) = 1 - [ ^{15} C _ 0 * (0.20)^{0} * (0.80 )^{15}]

P(r \ge 1 ) = 1 - 0.0352

P(r \ge 1 ) = 0.9648

4 0
1 month ago
100 point!!!
Leona [12618]

Answer:

45 grams

Step-by-step explanation:

1st order: 27 people

15 people:

100 g

Ginger: 20 g

Turmeric: 25 g

Coriander: 35 g

Cumin Seeds: 20 g

20+25+35+20=60+40=100

For 1 person:

Ginger: 1 1/3 g

Turmeric: 1 2/3 g

Coriander: 2 1/3 g

Cumin Seeds: 1 1/3 g

Multiply the total by 27

For 27 people:

Ginger: 36 g

Turmeric: 45 g

Coriander: 63 g

Cumin Seeds: 36 g

45 g for Turmeric

4 0
20 days ago
the diameter of a cylindrical box of CDs is 5 inches. The height of the box is 4 inches. Whuch measurement is closest to the tot
Svet_ta [12734]
To calculate the area, simply multiply 5 by 4, resulting in 20.
5 0
29 days ago
Read 2 more answers
Leticia invests $200 at 5% interest. If y represents the amount of money after x time periods, which describes the graph of the
Leona [12618]

Answer:

First, it's essential to define the equation that characterizes the function.

The investment is $200 with an interest rate of 5%, where y represents the money after x periods.

After one period, the amount of money grows to 200 plus 5% interest, resulting in 200 + 5%(200) = 200 (1 +5%) = 200 (1 + 0.05) = 200 (1.05)

After two periods, the total is 200(1.05)*(1.05) = 200 (1.05)^2

After three periods, it will be 200 (1.05)^3

Consequently, it can be inferred that after x periods, y = 200 (1.05)^x

Next, this function can be analyzed to project the graph's shape and significant points.

The answers derive from the initial value and the growth factor.

The initial value occurs when x = 0, giving y = 200 (1.05)^0 = 200*1 = 200

The growth factor is 1.05, indicating each subsequent value is multiplied by 1.05.

Step-by-step explanation:

3 0
17 days ago
Read 2 more answers
Miguel spends $100 on books, five of which are hardcover and the remaining four are paperback. The prices at the bookstore are b
babunello [11817]

Answer:

$10

Step-by-step explanation:

Each hardcover book costs $12, resulting in a total of $60 for five of them out of $100. The remaining four paperbacks at $10 each amount to a total of $40.

I hope this was helpful!!!:)

6 0
2 months ago
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