1. a.Solution: There are 513 Canadian people in 1000 people in a large city.The probability that a person, selected at random from population has a Canadian background is:.513.01000513PAnswer: 0.513.1. b.Solution: There are 72 African people in 1000 people in a large city.The probability that a person, selected at random from population has a Canadian background is:.072.0100072PAnswer: 0.072.1. c.Solution: There are 211789100056721485131000African people in 1000 people in a large city.The probability that a person, selected at random from population has a Canadian background is:.211.01000211PAnswer: 0.211.2. a.Solution: The probability of spinning A on the first spin is the same as of spinning B and C as well: .%3.333333.031PAnswer: %3.333333.031.
2. b.Solution: The tree diagram:2. c.Solution: The probability of spinning A followed by B is: .%1.111111.0913131PAnswer: %3.333333.031.2. d.Solution: The outcomes with the same letter on both spins are: (A, A), (B, B), (C, C).So, the probability of getting the same letter on both spins is: .%3.333333.03193919191PAnswer: %1.111111.091.
3.Solution: The binomial distributionis a type of discrete probability distribution with parameters nand pof the number of successes in a sequence of nindependent experiments with two possible outcomes, each of which has the probability of success p. For example, a coin toss has only two possible outcomes: heads or tails and taking a test could have two possible outcomes: pass or fail.Binomial distributions are used in the following conditions:1. The number of observations is fixed because if we repeat the experiment many times the probability of getting a success will be very close to 100%.2. The observations are independent. 3. The probability of success doesn’t change from one trial to another.The formula of binomial distribution is:knkpp1CnofoutkPnk– the probability of getting exactly ksuccesses in ntrials.Example: We throw a die. The probability of throwing even number is 50%. The probability of getting exactly keven numbers in ntrials can be found with the formula of binomial distribution.
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- Fall '16