Question

Marcia and John are playing the following game: Marcia thinks of a fraction, and John flips a coin. If the coin turns up heads, Marcia multiplies the number she's thinking of by $\frac{7}{8}$. If the coin turns up tails, she multiplies the number she's thinking of by $\frac{8}{7}$. John flips the coin ten times, and after each flip Marcia multiplies the number in her head by either $\frac{7}{8}$ or $\frac{8}{7}$, depending on the coin flip. The ten coin flips turn out to be:$\[\text{HHHTHTTTHH},\]$where H means 'heads' and T means 'tails.' What number is Marcia thinking of at the end of the game if she starts out with the fraction $\frac{1}{3}$?
Plz Hlp 4 HW

Answer 1

Using proportions, it is found that the number she is thinking at the end of the game is of $\frac{49}{192}$.

What is a proportion?

A proportion is a fraction of a total amount, and the measures are related using a rule of three.

In this problem, there are 6 heads and 4 tails, hence:

• She multiplies by 7/8 six times.

• She multiplies by 8/7 four times.

Hence the number she will be thinking is:

$n = \frac{1}{3} \times \left(\frac{7}{8}\right)^6 \times \left(\frac{8}{7}\right)^4 = \frac{1}{3} \times \left(\frac{7}{8}\right)^2$

$n = \frac{49}{192}$

More can be learned about proportions at https://brainly.com/question/24372153

#SPJ1