There are these two sets of letters, and you are going to pick exactly...
P(at least one vowel) = 1 – P(no vowels)
The probability of picking no vowel from the first set is 3/5. The probability of picking no vowel from the second set is 5/6. In order to get no vowels at all, we need no vowels from the first set AND no vowels from the second set. According to the AND rule, we multiply those probabilities.
P(no vowels) = (3/5)*(5/6) = 1/2
P(at least one vowel) = 1 – P(no vowels) = 1 – 1/2 = 1/2
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There are these two sets of letters, and you are going to pick exactly...
Explanation:
Understanding the Sets:
- Set 1: {a, e, i, o, u}
- Set 2: {b, c, d, f, g, h, j, k, l, m, n, p, q, r, s, t, v, w, x, y, z}
Finding the Probability:
- To find the probability of picking at least one vowel, we need to consider all possible outcomes when picking one letter from each set.
- Total number of outcomes = 5 (from Set 1) * 20 (from Set 2) = 100
Finding the Number of Outcomes with at least one Vowel:
- Number of outcomes with at least one vowel = Total number of outcomes - Number of outcomes with no vowels
- Number of outcomes with no vowels = 15 (from Set 1) * 20 (from Set 2) = 300
- Number of outcomes with at least one vowel = 100 - 300 = 70
Calculating the Probability:
- Probability of picking at least one vowel = Number of outcomes with at least one vowel / Total number of outcomes
- Probability = 70 / 100 = 7 / 10 = 0.7 = 1/2
Therefore, the probability of picking at least one vowel when choosing one letter from each set is 1/2 or 50%. So, the correct answer is option 'c) 1/2'.