Selecting a letter of the alphabet: If 3 letters of the alphabet are selected at random, find the probability of getting at least one letter "x". Letters can be used more than once.

My answer was: P(at least 1 "x) = 1 - (25/26)^3 = 1951/17576 or 0.11

Is this correct?

Most problems of the "at least" type are best done by subtracting from total.

P(at least one x) = 1 - P(no x's) = 1 - (25/26)^3 = 0.111 (3dp)

So, Yes, you are correct.

Well, well, well! Probability is always a fun game. Let's see if you found the right answer.

You're almost there with your calculation, but not quite spot-on. The probability of getting at least one "x" when selecting 3 letters at random can be found using the complement rule.

The probability of not getting any "x" in a single selection is 25/26, as there are 25 letters that are not "x" out of a total of 26 letters.

To find the probability of not getting any "x" in three selections, we multiply the probabilities together, like so: (25/26)^3.

Now, the probability of getting at least one "x" is simply the complement of not getting any "x." So, we subtract this probability from 1.

Let's calculate it: 1 - (25/26)^3 ≈ 0.1164 or approximately 11.64%.

Your answer of 0.11 is a bit off, but you were close! Keep those calculators handy and embrace the randomness!

To calculate the probability of getting at least one letter "x" when selecting 3 letters of the alphabet, you can use the principle of complementary probability. This means you find the probability of the complementary event (not getting any letter "x") and subtract it from 1.

The probability of not getting any letter "x" in one selection is 25/26 (since there are 25 letters without "x" out of 26 total letters in the alphabet). Since the selections are independent, we need to raise this probability to the power of 3 to account for all three selections.

So, the probability of not getting any letter "x" in all three selections is (25/26)^3.

To find the probability of getting at least one letter "x," we subtract the probability of not getting any letter "x" from 1:

P(at least 1 "x") = 1 - (25/26)^3 = 1 - 0.9352 ≈ 0.0648.

Therefore, the correct probability is approximately 0.0648, or about 6.48%.

To find the probability of getting at least one letter "x" when 3 letters of the alphabet are selected at random, we can use the concept of complementary probability. The complementary probability is the probability of the event not happening.

To solve this problem, we need to find the probability of not getting any "x" in the three selections, and then subtract it from 1 to get the probability of getting at least one "x".

The total number of letters in the alphabet is 26. Since letters can be used more than once, the total number of possible outcomes for each selection is also 26.

The probability of not getting an "x" in a single selection is (25/26), as there are 25 letters (excluding "x") out of 26 possible choices.

To find the probability of not getting an "x" in all three selections, we multiply the probabilities together: (25/26) * (25/26) * (25/26) = (25/26)^3.

Finally, to find the probability of getting at least one "x", we subtract the probability of not getting any "x" from 1:

P(at least 1 "x") = 1 - (25/26)^3.

Calculating this expression, we get:

P(at least 1 "x") = 1 - (15625/17576) = 1951/17576 ≈ 0.11.

So, your answer of P(at least 1 "x") = 1951/17576 or approximately 0.11, is correct.