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Math 375 Exam 1 1. (10 points) A die is thrown 5 times. What is the probability

ID: 3305423 • Letter: M

Question

Math 375 Exam 1 1. (10 points) A die is thrown 5 times. What is the probability that numbers 1 and 6 occur at least once? 2. (10 points) You toss a coin three times. Given that you have obeerved at least one heads, what is the probability that you observe at least two heads? 3. (10 points) I roll a fair die twice and obtain two numbers: z result of the first roll and z result of the second roll Given that I know yy7 what is the probability that 3 or 37 4. (10 points) The weatherman has predicted rain for tomorrow. When it actually rains, the weatherman correctly forecasts rain 90% of the time, when it does not rain, he incorrectly forecasts rain 10% of the time, what is the probability that it will rain tomorrow? 5. (10 points) A father of two children is picked at random. He then tells you, "I have two children, and one of them is a girl born on a Tuesday." Assuming he is telling the truth, what is the probability that his second child is also a girl?

Explanation / Answer

Q3) Since we know that the sum is 7, then to get 7 the following are possible total outcomes (1,6), (6,1), (2,5), (5,2), (3,4), (4,3) i.e 6 outcomes

Out of these 6 outcomes, only 2 of them are my favourable outcomes i.e, (3,4), (4,3)

Therefore my required probability = 2/6 = 1/3