Demetri has trouble spelling the word “banana.” Whenever he tries to spell the word, he writes the letters “ba,” then...

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Demetri has trouble spelling the word “banana.” Whenever he tries to spell the word, he writes the letters “ba,” then writes “na” one or more times, then stops. Every time Demetri writes the letters “na” there is a 60% chance that he will write the letters “na” again (otherwise he stops). When Demetri tries to spell the word “banana,” what percent of the time does Demetri spell “banana” correctly?

A. 14.4%
B. 24%
C. 36%
D. 40%
E. 60%

Answer: B

Source: Veritas Prep
Source: — Problem Solving |

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To spell banana correctly, he has to write "na" twice, in order, and then stop.

The probability of the first "na" is 1.

The probability of the second "na" is .6

Now, he needs to stop in order to spell the word correctly.

There is a 40% chance of stopping after writing a "na".

So the total probability is 1*.6*.4= .24, B