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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.
In this problem, the total number of possibilities is 20, so n = 20.The set of prime numbers from 1 to 20 = {2, 3, 5, 7, 11, 13, 17, 19}, so f = 8Probability = f/n = 8/20 = 0.4.You have a 2 in 5 chance of choosing a prime number from 1 to 20.
It depends on what variable the probability ratio was for! The random variable could have been the number of heads minus the number of tails, for example.
The result of tossing the coin would not affect which number was selected. So we say that these two events are independent. We can therefore assess the probability of each of them separately and then multiply the two probabilities together for a final result. Probability of getting tails: 1/2 (since there is one way of getting heads out of two possibilities) Probability of getting zero: 1/10 (since there is one way of getting zero out of ten possibilities) Overall probability: 1/2 x 1/20 = 1/20
The first prime after 20 is 23.