All categories

3 years ago

A fair coin is tossed 10 times. What is the probability that two heads do not occur consecutively?

Mathematics

1 answer:

alexira [117]3 years ago

5 0

Answer:

0.140625

Step-by-step explanation:

Total numbers of possible combinations for a coin = 2^n

If the coin is tossed 10 times, we have 2^10 = 1024

If the coin is tossed once, we have 2^1 = 2 outcomes.

The possible outcomes are H, T.

We have 2 outcomes with no two consecutive head.

If the coin is tossed twice, we have 2^2 = 4 outcomes.

The possible outcomes are HH, HT, TH, TT

We have 1 outcome with two consecutive heads and 3 outcomes without two consecutive heads.

If the coin is tossed thrice, we have 2^3 = 8 outcomes.

The possible outcomes are HHH, HHT, HTH, HTT, TTH, THT, THH and TTT

We have 3 outcomes with two consecutive head and 5 outcomes without two consecutive heads.

Comparing the results from the outcomes of the coin,we have 2,3,5,......

This looks like a financial sequence. For the next 10 tosses, we have

2,3,5,8,13,21,34,55,89,144

We have 144 outcomes without two consecutive heads if the coin is tossed 10 times

Pr(number of two consecutive Heads in 10 tosses) = 144/1024

= 0.140625

You might be interested in

Izumi is running on a quarter-mile oval track. After running 110 yards, his coach records his time as 16 seconds.

pickupchik [31]

Answer:

14.04 miles per hour

Step-by-step explanation:

The problem is asking for Izumi's speed. The formula of speed is:

s = $\frac{d}{t}$ , where "s" means speed, "d" means distance and "t" means time.

The problem is also asking for the unit miles per hour ( $\frac{miles}{hour}$ ) so, this means that we have to know how many miles Izumi ran, given that the problem only mentioned yards (110 yards).

Let's convert 110 yards to miles, provided that he Izumi ran 1,760 yards in a mile.

110 yards ÷ 1760 $\frac{yards}{mile}$ = 0.0625 miles (this is the distance covered by Izumi in miles)

Let's go back again to the formula: s = $\frac{d}{t}$

s = $\frac{0.0625 miles}{16 seconds}$ = 0.0039 $\frac{miles}{sec}$

Since, the we arrived at a miles per second unit, we have to convert it to miles per hour.

So, if a minute has 60 seconds, then an hour has 3,600 seconds.

Thus, 0.0039 $\frac{miles}{sec}$ × 3,600 $\frac{seconds}{hour}$ = 14.04 miles per hour (the answer)

3 0

3 years ago

Use mathematical induction to prove that if L is a linear transformation from V to W, then L (α1v1 + α2v2 +· · ·+αnvn)= α1L (v1)

e-lub [12.9K]

Answer:

The proof is shown in the explanation below.

Step-by-step explanation:

Analysis:

The proof by induction focuses on n. In this case, let n = 1, and $L^{1}$ will be a linear operator since $L^{1} = L$

The exercise will show that $L^{n}$ is a linear operator on V and that $L^{n+1}$ is also a linear operator on V. This, follows that:

$L^{n+1} (av) = L(L^{m}(v_{1}+v_{2})\\ = L(L^{m} (v_{1} + L^{m}v_{2})\\ = L(L^{m}v_{1} + L(L^{m}v_{2})\\ = L^{m+1}(v_{1}) + L^{m+1}(v_{2})$

6 0

3 years ago

Read 2 more answers

????????!1!!!!!!! HELPPPPPPPPPPP

pav-90 [236]

Answer:

Step-by-step explanation:

Let us say, Olivia's age is x.

Now as the question says, we will get this equation.

$( \frac{1}{3} x ) + 12= 2x - 3$

Multiply both sides by 3.

$x + 36 = 6x - 9$

Collect like terms.

$x - 6x = - 9 - 36$

Calculate.

$- 5x = - 45$

Divide both sides of the equation by -5.

$x = 9$

Then, we will get the answer.

I hope it helps.

8 0

2 years ago

Scientists in Florida are measuring the masses of sea turtles as they hatch. They create a line graph and plots the masses of 18

NeTakaya

Answer:

36 3/4

Step-by-step explanation:

12 1/4 + 12 1/4 + 12 1/4 = 36 3/4 :)

8 0

3 years ago

PLEASE HELP ME THIS QUESTION! I'LL VOTE YOU BRAINLETS!

d1i1m1o1n [39]

Answer:

see below

Step-by-step explanation:

Let's add the amounts earned together to find his total earnings. This is 60 + 84 + 72 + 96 + 48 = $360. If he had $218 left over the skis cost 360 - 218 = $142.

7 0

3 years ago