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4 years ago

6

Alice and bob play a simple dice game. they take turns rolling a single die, starting with alice, until one of them wins by gett

ing a 6. in the end it turns out that bob won. what is the probability that he won on his first roll

2 answers:

Cerrena [4.2K]4 years ago

6 0

Answer:

<h2>Bob has 16.67% of winning the game at his first roll.</h2>

Step-by-step explanation:

According to the problem, they are playing with a simple dice, which means it has 6 possible outcomes 1, 2, 3, 4, 5 and 6.

The one that gets 6 wins.

To find the probability of winning the first Bob's roll, we just need to find the simple probability of getting 6, which is

$P=\frac{1}{6}$

Therefore, Bob has 16.67% of winning the game at his first roll.

Delicious77 [7]4 years ago

3 0

The probability he won on his first roll is 1/6.

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Evaluate the line integral, where C is the given curve. (x + 6y) dx + x2 dy, C C consists of line segments from (0, 0) to (6, 1)

Dima020 [189]

Split $C$ into two component segments, $C_1$ and $C_2$ , parameterized by

$\mathbf r_1(t)=(1-t)(0,0)+t(6,1)=(6t,t)$

$\mathbf r_2(t)=(1-t)(6,1)+t(7,0)=(6+t,1-t)$

respectively, with $0\le t\le1$ , where $\mathbf r_i(t)=(x(t),y(t))$ .

We have

$\mathrm d\mathbf r_1=(6,1)\,\mathrm dt$

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where $\mathrm d\mathbf r_i=\left(\dfrac{\mathrm dx}{\mathrm dt},\dfrac{\mathrm dy}{\mathrm dt}\right)\,\mathrm dt$

so the line integral becomes

$\displaystyle\int_C(x+6y)\,\mathrm dx+x^2\,\mathrm dy=\left\{\int_{C_1}+\int_{C_2}\right\}(x+6y,x^2)\cdot(\mathrm dx,\mathrm dy)$

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$=\displaystyle\int_0^1(35t^2+55t-24)\,\mathrm dt=\frac{91}6$

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3 years ago

Suppose there is a bag containing 5 red marbles (Upper R), 5 pink marbles (Upper P), 5 green marbles (Upper G), and 5 blac

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Answer:

In the Explanation

Step-by-step explanation:

(a)From the attached probability tree, the possible outcomes are:

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(b)Probability Distribution of Drawing Pink Marbles

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3 years ago

Sam is at the top of a tower and will ride down a zip line to a lower tower. The total vertical drop of the zip line is 40 ft. T

jek_recluse [69]

Answer:

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Since the vertical distance between the two tower = 40ft

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The horizontal distance between the two towers = x

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Check attached document for better illustration of the triangle.

Tanθ = opposite / adjacent

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3 years ago

PLEASE HELP NOW --- >N is a 2-digit even number. If the last two digits of N^2 is the same as N, what is the sum of digits of

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Answer:

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4 years ago

A movie theater has a 24-foot-high screen located 6 feet above your eye level. If you sit x feet back from the screen, your vi

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Answer:

The viewing angles are as follows:

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For x=15 feet, θ = 0.726 radians

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For x=25 feet, θ = 0.640 radians

Step-by-step explanation:

The viewing angle is given as:

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= 1.4056 - 0.8761

θ = 0.529 radians

<u>For x = 10 feet:</u>

θ = tan⁻¹(30/10) - tan⁻¹ (6/10)

= 1.249 - 0.540

θ = 0.708 radians

<u>For x = 15 feet:</u>

θ = tan⁻¹(30/15) - tan⁻¹ (6/15)

= 1.107 - 0.380

θ = 0.726 radians

<u>For x = 20 feet:</u>

θ = tan⁻¹(30/20) - tan⁻¹ (6/20)

= 0.983 - 0.291

θ = 0.691 radians

<u>For x = 25 feet:</u>

θ = tan⁻¹(30/25) - tan⁻¹ (6/25)

= 0.876 - 0.235

θ = 0.640 radians

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3 years ago