Write and expression to represent the submarines elevation after its final dive

If a fair coin is flipped 15 times, what is the probability that there are more heads than tails?

ludmilkaskok [199]

Answer:

The probability that there are more heads than tails is equal to $\dfrac{1}{2}$ .

Step-by-step explanation:

Since the number of flips is an odd number, there can't be an equal number of heads and tails. In other words, there are either

more tails than heads, or,
more heads than tails.

Let the event that there are more heads than tails be $A$ . $\lnot A$ (i.e., not A) denotes that there are more tails than heads. Either one of these two cases must happen. As a result, $P(A) + P(\lnot A) = 1$ .

Additionally, since this coin is fair, the probability of getting a head is equal to the probability of getting a tail on each toss. That implies that (for example)

the probability of getting 7 heads out of 15 tosses will be the same as
the probability of getting 7 tails out of 15 tosses.

Due to this symmetry,

the probability of getting more heads than tails (A is true) is equal to
the probability of getting more tails than heads (A is not true.)

In other words $P(A) = P(\lnot A)$ .

Combining the two equations:

$\left\{\begin{aligned}&P(A) + P(\lnot A) = 1 \cr &P(A) = P(\lnot A)\end{aligned}\right.$ ,

$P(A) = P(\lnot A) = \dfrac{1}{2}$ .

In other words, the probability that there are more heads than tails is equal to $\dfrac{1}{2}$ .

This conclusion can be verified using the cumulative probability function for binomial distributions with $\dfrac{1}{2}$ as the probability of success.

$\begin{aligned}P(A) =& P(n \ge 8) \cr =& \sum \limits_{i = 8}^{15} {15 \choose i} (0.5)^{i} (0.5)^{15 - i}\cr =& \sum \limits_{i = 8}^{15} {15 \choose i} (0.5)^{15}\cr =& (0.5)^{15} \left({15 \choose 8} + {15 \choose 9} + \cdots + {15 \choose 15}\right) \cr =& (0.5)^{15} \left({15 \choose (15 - 8)} + {15 \choose (15 - 9)} + \cdots + {15 \choose (15 - 15)} \right) \cr =& (0.5)^{15} \left({15 \choose 7} + {15 \choose 6} + \cdots + {15 \choose 0}\right)\end{aligned}$

$\begin{aligned}\phantom{P(A)} =& \sum \limits_{i = 0}^{7} {15 \choose i} (0.5)^{15}\cr =& P(n \le 7) \cr =& P(\lnot A)\end{aligned}$ .

6 0

3 years ago

A small town surveys 250 adults, 180 of which are parents, about whether or not a park should be expanded. The results showed th

andrew-mc [135]

250 adults and 180 of which are parents, so 250 -180 = 70 are not parents. <span>The results showed that 150 of the adults with children and 40 of those without thought the park should be expanded. So there are 180 – 150 = 30 parents who answered no. and 70 – 40 = 30 not parents who answered no.</span> <span>
yes | no
parents 150 | 30
not parents 40 | 30

</span>

3 0

3 years ago

In this triangle, what is the value of x? Enter your answer, rounded to the nearest tenth, in the box. x = yd A right triangle w

Eduardwww [97]

Answer: 47.4 yds.

So, if this is a right triangle then you will have a hypotenuse, opposite Leg, and the adjacent. I get it that the first Leg is X an the other is 40 and the hypotenuse is 62.

C=62

A=40

B= X

We gonna use the Pythagorean theorem to solve this problem

C^2=a^2+b^2

62^2=40^2+x^2

x^2 = (62^2) -(40^2)

x^2= 3844-1600

x^2= 2244

x= 47.3708771293

7 0

3 years ago

Read 2 more answers

Can someone pls help

Luba_88 [7]

I believe the correct answer would be 5,1,3 :)

3 0

2 years ago

Read 2 more answers

Inessa ran 3 laps in 8 minutes. How long would it take her to run 10 laps at this pace? (This is proportions)

Degger [83]

Answer:

26.6 minutes

Step-by-step explanation:

Set up a proportion

3/8 = 10/x

cross multiply

3x = 80

x = 26.6

5 0

3 years ago