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AleksandrR [38]
3 years ago
6

Alice and Bob are playing a game. Alice starts first. On Alice's turn, she flips a coin. If she gets a heads, she wins. If not,

it becomes Bob's turn. On Bob's turn, he flips a coin. If he gets a tails, he wins. If not, it becomes Alice's turn. What is the probability that Alice wins the game?
Mathematics
1 answer:
trapecia [35]3 years ago
8 0

Answer:

The probability that Alice wins the game=\frac{1}{2}

Step-by-step explanation:

We are given that Alice and Bob are playing a game .

We have to find the probability that Alice wins the game .

If Alice win when she gets head and lose when she gets tail.Bob wins when she gets tail and she lose when she gets head.

Total results in a coin=Head, tail=2

Number of head in a coin=1

Number of tail in a coin= 1

Probability is defined as the possibility of an event that occurred

P(E)=\frac{Number\;of\;favourable\;cases}{total\;of\;cases}

The probability that Alice wins the game=\frac{Number\;of\;favourable\;cases}{Total\;number\;of\;cases}

The probability that Alice wins the game=\frac{number \;of \;heads}{Total\; results}

The probability that Alice wins the game=\frac{1}{2}

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Express 11011 in base two ​
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Step-by-step explanation:

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2 years ago
Compare -1.5 and -4.5
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Answer:

-3

Step-by-step explanation:

There's a three point distance between the two on a coordinate plane

3 0
2 years ago
The graph shows the functions f(x), p(x), and g(x): Graph of function g of x is y is equal to 1 plus the quantity 1.5 raised to
satela [25.4K]
Part A:

Given that the <span>straight line p(x) joins the ordered pairs (0, 2) and (1, -5), thus the equation of the line joining ordered pairs (0, 2) and (1, -5) is given by

\frac{y-2}{x} = \frac{-5-2}{1} =-7 \\  \\ \Rightarrow y-2=-7x \\  \\ \Rightarrow y=-7x+2

Thus, p(x) = -7x + 2

</span>Given that the <span>straight line f(x) joins the ordered pairs (4, 1) and (2, -3), thus the equation of the line joining ordered pairs (4, 1) and (2, -3) is given by

\frac{y-1}{x-4} = \frac{-3-1}{2-4} =\frac{-4}{-2}=2 \\  \\ \Rightarrow y-1=2(x-4)=2x-8 \\  \\ \Rightarrow y=2x-7

Thus, f(x) = 2x - 7
</span>
The solution to the pair of equations represented by p(x) and f(x) is given by

p(x) = f(x)
⇒ -7x + 2 = 2x - 7
⇒ -7x - 2x = -7 - 2
⇒ -9x = -9
⇒ x = -9 / -9 = 1

Substituting for x into p(x), we have

p(1) = -7(1) + 2 = -7 + 2 = -5

Therefore, the solution to the pair of equations represented by p(x) and f(x) is  (1, -5)



Part B:

From part A, we have that f(x) = 2x - 7

when x = -8

f(-8) = 2(-8) - 7 = -23

Thus, (-8, -23) is a solution to f(x).

When x = -10

f(-10) = 2(-10) - 7 = -27

Thus, (-10, -27) is a solution to f(x).

Therefore, two solutions of f(x) are (-8, -23) and (-10, -27).



Part C:

From part A, we have that p(x) = -7x + 2, given that g(x) = 1 + 1.5^x

From the graphs of p(x) and g(x), we can see that the two graphs intersected at the point (0, 2).

Therefore, the solution to the equation p(x) = g(x) is (0, 2).

3 0
3 years ago
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