Probability Bonus How to Solve (May not be on quiz)

A bag contains 14 blue, 6 red, 12 green, and 8 purple buttons. 25 buttons are removed from the bag randomly. How many of the removed buttons were red if the chance of drawing a red button from the bag is now 1/3?

Initially there are 6 red buttons out of 40 total. After removing 25, 15 remain. Let 𝑟r be the number of removed red buttons, so 6−𝑟 red remain. So, 6 -r/15 = 1/3 (the new chance). Multiply 15 times 1 and divide by 3. That gives 5. 5 is r. 6 -5 =1.

Therefore, 1 red button was removed.

In a lottery game, each ticket has a 2% chance of winning. If a man buys 10 tickets, what is the probability that at least one of them wins?

The chance of winning any one ticket is 0.02. The probability of at least one win in 10 tickets is: 1 - (1-.02)^10.

That simplifies to 1 - (.98)^10

Then to 1 - .817 = .183

183% is final answer

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