The sample space consists of the letters of the word "PROBABILITY" = {P,R,O,B,A,I,L,T,Y}
The sample space for choosing a letter from the word SPACE is {S, P, A, C, E}. The sample space for choosing a consonant from the word MATH is {M, T, H}. Consonants are letters that are not vowels (A, E, I, O, U), so in the word MATH, the consonants are M, T, and H.
11 * * * * * No, on two counts. The sample space is the possible outcomes of the experiment, not the NUMBER of possible outcomes. And, as far as this experiment is concerned, there is no way to distinguish between the two occurrences of b and i. So there are, in fact, only 9 possible outcomes. Two of these outcomes have a higher probability but that is a different matter. The sample space is {p, r , o , b, a, i, l, t, y} a set of cardinality 9.
Associates a particulare probability of occurrence with each outcome in the sample space.
sample space
3/4
The sample space is {m, a, t, h, e, i, c, s} which, curiously, is also the sample space for choosing a letter from my user name!
Probability of choosing a consonant from math = 3/4
If you have an equal amount of odd and even numbers in a determined sample space, the probability of choosing and odd number is 1/2 (.5).
The word "space" consists of 5 letters: s, p, a, c, and e. If you are choosing one letter at random from these 5 letters, the probability of choosing any specific letter is 1 out of 5, or 20%. If you're looking for the probability of choosing a vowel (a or e), it would be 2 out of 5, or 40%.
In the sample space [1,20], there are 8 prime numbers, [2,3,5,7,11,13,17,19]. The probability, then, of randomly choosing a prime number in the sample space [1,20] is (8 in 20), or (2 in 5), or 0.4. The probability of choosing two of them is (8 in 20) times (7 in 19) which is (56 in 1064) or (7 in 133) or about 0.05263.
The sample space is {p, r, o, b, a, i, l, t, e, s}
The sample space for choosing a letter from the word SPACE is {S, P, A, C, E}. The sample space for choosing a consonant from the word MATH is {M, T, H}. Consonants are letters that are not vowels (A, E, I, O, U), so in the word MATH, the consonants are M, T, and H.
11 * * * * * No, on two counts. The sample space is the possible outcomes of the experiment, not the NUMBER of possible outcomes. And, as far as this experiment is concerned, there is no way to distinguish between the two occurrences of b and i. So there are, in fact, only 9 possible outcomes. Two of these outcomes have a higher probability but that is a different matter. The sample space is {p, r , o , b, a, i, l, t, y} a set of cardinality 9.
Associates a particulare probability of occurrence with each outcome in the sample space.
Discrete probability. It helps if the all the outcomes in the sample space are equally probable but that is not a necessity.
sample space
3/4