250 Grade 10 students, 120 liked mathematics (M), 160 liked science (S) and 75 liked both mathematics and science. a) Draw a Venn diagram illustrating this problem. If a student is selected from this group, what is the probability that: b) he/she liked mathematics or science? c) he/she did

A survey was done in regards to what type of animals are preferred as pets. Each respondent selected their top choice of animal for a pet. Respondents selected from: dog, cat, farret, fish, and bird.  After the survey was completed, 41% picked dog, 34% picked cat, 4% picked farret, 8% picked fish, and 13% picked bird.  Suppose three respondents were chosen at random. What is the probability that AT LEAST ONE of them picked dog?  Round the answer to 3 decimal places.

3. The latest data from the CDC indicates that 14% of Americans are smokers. A researcher wants to identify smokers for a survey. He randomly selects people entering a grocery store to ask if they are a smoker. a) What is the probability that he identifies the first smoker on his 5th try? b) What is the probability that he has to approach more than 8 people before finding the first smoker? c) How many people does he expect to approach before finding the first smoker?

In a​ lottery, the top cash prize was $675 million dollars, going to three lucky winners. Players pick four different numbers 1 to 58 and  one number 1 to 48.  A player wins a minimum of $100 by correctly matching two numbers drawn from the white balls (1 through 58) and matching the number on the gold bal (1 through 48).  What is the probability of winning the minimum award?