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

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

2. On tossing a coin three times, the sample space will be:

{HHH, HHT, HTH, THH, TTH, THT, HTT, TTT} Where H is heads and T is tails.

So,

P(At leaast one head) = 7/8

P(At least two heads) = 4/8

Therefore,

P(At least two heads| At least one head) = (4/8)/(7/8) = 4/7

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