1)A two-figure number is written down at random. Find the probability that
a)the number is greater than 44
b)the number is less than 100
2)A letter is picked at random from the english alphabet. Find the probability that
a)the letter is a vowel (my answer=5/26)
b)the letter comes in the first half of the alphabet (my answer=13/26)
c)the letter is one that appears in the word PROBABILITY
3)A letter is chosen at random from the letters of the word SUCCESSION. What is the probability that the letter is (a)N (b)S (c)vowel (d) not S
Please help
1. 10-99 are two digits # and that mean there are 99-10+1=90 possible numbers (and of course they're all less than 100). and so from 45-90, there are 46 numbers.
2. a and b looks right. There are 9 different letters in the word PROBABILITY so it should be 9/26.
3. Count the number of repeats in each letter within the word. For example, S repeats 3 times and the total letter is 10 thus the probably to draw an S from the word is 3/10... and so on for the rest of the problem.
Sure, I'd be happy to help you with these probability questions. Here's how you can find the answers:
1) Since a two-figure number is written down at random, there are 90 possible outcomes (from 10 to 99).
a) To find the probability that the number is greater than 44, we need to count the numbers from 45 to 99, which is a total of 55 numbers. So the probability is 55/90, which simplifies to 11/18.
b) To find the probability that the number is less than 100, we need to count all the numbers from 10 to 99, which is a total of 90 numbers. So the probability is 90/90, which simplifies to 1.
2) Since there are 26 letters in the English alphabet, we have 26 possible outcomes.
a) To find the probability that the letter is a vowel, we need to count the number of vowels (A, E, I, O, U) which is 5. So the probability is 5/26.
b) To find the probability that the letter comes in the first half of the alphabet, we need to count the number of letters from A to M, which is 13. So the probability is 13/26, which simplifies to 1/2.
c) To find the probability that the letter is one that appears in the word PROBABILITY, we count the number of unique letters in the word (P, R, O, B, A, I, L, T, Y), which is 9. So the probability is 9/26.
3) The word SUCCESSION has 10 letters, so there are 10 possible outcomes.
a) To find the probability that the letter is N, we count the number of Ns in the word, which is 1. So the probability is 1/10.
b) To find the probability that the letter is S, we count the number of Ss in the word, which is 3. So the probability is 3/10.
c) To find the probability that the letter is a vowel, we count the number of vowels in the word (U, E, I, O), which is 4. So the probability is 4/10, which simplifies to 2/5.
d) To find the probability that the letter is not S, we need to count the number of letters that are not S, which is 7 (U, C, C, E, I, O, N). So the probability is 7/10.
I hope this helps! Let me know if you have any more questions.