Keiko tosses one penny and Ephraim tosses two pennies. What is the probability that Ephraim gets the same number of heads that Keiko gets? Express your answer as a common fraction.

Guest Jul 3, 2019

#1**+7 **## \(-tommarvoloriddle\)

# EDIT:

## SUMMARY

\(Let\ K(n)\ be\ the\ probability\ that\ Keiko\ gets\ n\ heads,\ and\ let\ E(n)\ be\ the\ probability\ that\ Ephriam\ gets\\ \\ n\ heads. \\ \\ K(0) = 1/2 \\ \\K(1) = 1/2 \\ \\K(2) = 0\ (Keiko\ only\ has\ one\ penny!) \\ \\E(0) = \frac{1}{2}\cdot\frac{1}{2} = \frac{1}{4} \\ \\E(1) = \frac{1}{2}\cdot\frac{1}{2} + \frac{1}{2}\cdot\frac{1}{2} \\ \ \ \ \ \ \ \ \ = 2\cdot\frac{1}{4} \ \ \ \ \ \ \ \ = \frac{1}{2} \\ (because\ Ephraim\ can\ get\ HT\ or\ TH) \\ \\E(2) = \frac{1}{2}\cdot\frac{1}{2} = \frac{1}{4} \\ \\The\ probability\ that\ Keiko\ gets\ 0\ heads \\ \\ and\ Ephriam\ gets\ 0\ heads\ is\ K(0)\cdot E(0). \\ \\ Similarly\ for\ 1\ head\ and\ 2\ heads.\ Thus,\ we\ have: \\ \\P = K(0)\cdot E(0) + K(1)\cdot E(1) + K(2)\cdot E(2) \\ \\P = \frac{1}{2}\cdot\frac{1}{4} + \frac{1}{2}\cdot\frac{1}{2} + 0 \\ \\P = \frac{3}{8} \\ \\Thus\ the\ answer\ is\ 3/8.\)

- we used a equation K(0)*E(0)+K(1)+E(1)+K(2)*E(2)

- we found the values by using probability and logic.

- we plugged the numbers in

- we got the answer 3/8.

Apologises:

-quality of the answer

-all the work is in latex

-fact that it may not be super clear

If you have a question, just let me know.

.tommarvoloriddle Jul 3, 2019

edited by
tommarvoloriddle
Jul 3, 2019

edited by tommarvoloriddle Jul 3, 2019

edited by tommarvoloriddle Jul 3, 2019

edited by tommarvoloriddle Jul 3, 2019

edited by tommarvoloriddle Jul 3, 2019

#2**+2 **

Thanks Tom.....riddle

I'd just do it with a probablilty tree. Which is the same just more visual.

The first toss is Ephran1 , the second is Ephan2 and the last is Keiko's toss.

Which set of three branches gives the desired outcome?

Hint, there are 3 desirable branches ends and 8 ends altogether.

Melody Jul 3, 2019

#3**+5 **

In harry potter, You never hear the words: Thanks tom riddle.... LOL But better solution.

tommarvoloriddle
Jul 3, 2019