Demetri has trouble spelling the word “banana.” Whenever he tries to

Question

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%

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

LHC8717 · Answer

Demetria has to spell twice "na" to say banana correctly

Then there is 100% that we will write the first "na"
Then 60 % to write the second one
Then now, he has 40% to stop writing (100-60)

100% * 60% * 40% = 24% Answer B

BillyZ · Answer

OFFICIAL SOLUTION

In order for Demetri to spell "banana" correctly, he must write the letters "ba" (it is given that he will do so), and then write the letters "na" (it is also given that he will do this at least the first time), and then write the letters "na" again (this happens 60% of the time), and then not write the letters "na" again (this happens 100%−60%=40% of the time).

Thus, since "and" means "multiply," Demetri spells "banana" correctly 60%∗40%=24% of the time. This is B.

Fdambro294 · Answer

Demetri will write “ba”, then “na”

At this point, Demetri’s path splits in 2:

Path 1————> 60% of the time he will write “na” again

Path 2————>40% of the time he will STOP and spell the word incorrectly

Now following Path 1 towards the possibility of spelling the word Correctly, at this point his paths will Split again

Path 1A ————-> 60% of the time when he writes “na” he will write “na” again, thus misspelling the word

Path 1B ————-> 40% of the them when he writes “na” he will stop, and down this path he will spill the word CORRECTLY

In other words, the odds that he spells the word correctly are:

60 % chance he writes “na” (after already writing “ba” and “na)

and

From that point, 40% chance he just stops and ends up with the correct spelling

60% * 40% = .6 * .4 = .24 = 24%

There is a 24% chance that Demitri spells “banana” correctly.

-B-

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ScottTargetTestPrep · Answer

Solution:

The outcome in which “banana” is spelled correctly occurs when he writes the first “na” and the second “na” and then he stops writing. The probability that the first “na” is written is 100%, the probability that the second “na” is written is 60%, and the probability he stops writing at that point is 40%. Thus, the probability that “banana” is spelled correctly is 1 x 0.6 x 0.4 = 0.24 = 24%.

Answer: B

sarthak1701 · Answer

Since he writes "na" one or more times, the probability of him writing "na" at least once is 100%. Once he writes "na" for the first time, the probability of writing "na" drops to 60%, which means the probability of him not writing it after the first time is 40%. To write the correct spelling, we need to write "na" twice. The first time is 100% probability, and the second time the probability drops to 60%. After the second time, we don't need to write "na" again, so we multiply by the probability of not writing "na," which is 40%.

= 100%*60%*40% = 24%. Ans B

= 100%*60%*40% = 24%. Ans B

Demetri has trouble spelling the word “banana.” Whenever he tries to

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