Mathematics, 21.12.2019 01:31 braydentillery1221

You want to make five-letter codes that use the letters a, f, e, r, and m without repeating any letter. what is the probability that a randomly chosen code starts with m and ends with an e

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Prob( picking an M first) = 1/5

Now we require the sequence not e, not e, not e .

= 3/4 * 2/3* *1/2

So required probability = 1/5 * 3/4 * 2/3 * 1/2 = 6/120 = 1/20

Answer from: strevino9178

Given: Five letter codes are to be made with the letter A, F, E, R and M without repitition.

To Find: Probability that a randomly chosen code starts with M and ends with E.

Solution: So, required probability is $\frac{1}{20}$ .

Calculation/Explanation:

Let us calculate the required probability step-wise.

To pick the first letter as M, there are 5 possible outcomes (A, F, E, R or M) and picking M is only one possibility out 5 outcomes.

So, probability of picking an M first is equal to $\frac{1}{5}$ ...(1)

After this, in the second, third and fourth places, we must not pick an E. In the second place, there are 4 possible outcomes (A, F, E or R) out of which not picking an E means there are 3 possibilities (A, F or R) out of the 4 outcomes. So, for the second letter the probability of not picking an E is $\frac{3}{4}$ ...(2)

For the third letter, there are now 3 possible outcomes (since out 5 letters, 2 have already been chosen). One of these outcomes is an E and two will be non-E. This means, probability of not drawing an E is $\frac{2}{3}$ ...(3)

For the fourth letter, there are now 2 possible outcomes out of which one is an E and one is not an E. This means, the probability of not picking an E is $\frac{1}{2}$ ...(4)

For the final letter, only one possible outcome remains which is E. And therefore the probability that we draw an E would be 1 ...(5)

To get the total probability of starting the code with M and ending with E, we multiply the individual probabilities i.e., (1), (2), (3), (4) and (5).

So, required probability is $\frac{1}{20}$ .

Answer from: Quest

the law of definite proportions states samples of a compound will always contain the same proportion of elements by mass. in other words, a given compound will always contain the same elements in the same proportions by mass.the law of multiple proportions states when two elements combine with each other to form more than one compound, then the weights of one element that combine with a fixed weight of the other are in a ratio of small whole numbers.

Answer from: Quest

step-by-step explanation:

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You want to make five-letter codes that use the letters a, f, e, r, and m without repeating any lett...