Honors Mathematical Analysis Section 1.3: Introduction to Probability Q Problems Q1.) To the nearest hundredth, find 11.9% of 87.6. Q2.) 40% of a number is 24. What is the number? Q3.) Convert to scientific notation: 12,576. Q4.) A car travels 220 miles in 4 hours. What is its velocity? Q5.) Solve for all possible solutions of x: |x – 5| = 12 Q6.) Write in simplified radical form: Q7.) A parallelogram with a right angle must be classified as a: Q8.) What kind of angles are <1 and <2?
Q9.) Two legs of a right triangle measure 10 and 24 inches. How long is the hypotenuse? Q10.) If the side lengths of a triangle are tripled, the area increases how many times?
1. If a fair die is rolled, determine the probability of: A) Rolling a 3 B) Rolling a 3 or a 5 C) Rolling an even number D) rolling a prime or an even number
2. Calculate the probability given the odds: A) 3:2 B) 2:5 C) 5:1
3. Calculate the odds given the probability: A) 8/15 B) 2/3 C) 1/5
4. Calculate the following probabilities resulting from flipping a coin using two methods: i) By creating a sample space ii) By showing how it can be calculated without using a sample space A) Flipping three heads in a row B) Flipping three of the same result in a row
C) Flipping at least two heads (on 3 flips)
5. Create a sample space to calculate the following probabilities on a roll of two fair dice: A) P(sum of 7) B) P(sum of 6) C) P(sum of 8) D) P(sum of 5)
E) P(sum of 3 or 6) F) P(sum of 13) G) P(sum of at least 10)
6.) Based on your sample space for #5, which is more likely – P(rolling a sum of 7) or P(rolling a sum of 3 or 4)?
7.) What is the probability of rolling a 2 on a die and then flipping a heads on a coin?
8. Carlos is trying to get dressed in the dark in his bedroom. His drawer has 5 black, 4 brown, and 3 white socks. A) How many socks does he have to draw to guarantee getting a pair of black socks? B) What is the probability he selects a black or brown sock? C) What is the probability he chooses two brown in a row without replacement? D) Determine the probability that he selects two socks of the same color. (Hint: Break down the problem into smaller parts using AND/OR!) E) Calculate the probability of NOT drawing a white sock on two draws (assume he does not replace the first sock). F) What is the probability he picks five black socks in a row? 9. A cooler of drinks contains 7 Cokes, 4 Sprites, and 6 root beers. Find each probability, assuming no replacement: A) P(Coke or Sprite) B) P(Coke, then a Sprite) C) P(Coke & Sprite, either order)
D) P(3 root beers in a row) E) P(Drawing three in a row without getting a Sprite)
F) P(At least one Sprite on three draws) (Be crafty!!)
10. The probability that a traffic light will be red is 30%. A) What is the probability of being stopped at the first light and not at the second? B) What is the probability of three red lights in a row? C) What is the probability of at least one green light out of three?
11. The probability that it will rain Sunday is 80%. The probability it will rain Monday is 60%. Determine: A) P(rains both days) B) P(rains Sunday, not Monday)
C) P(rains neither day) D) P(rains Sunday or Monday, but not both) E) P(rains at least one of the two days)
12. If Joey Votto’s batting average is .320 (he gets a hit 32% of the time), what is the probability: A) He gets two hits in a row B) He gets out two at-bats in a row C) He gets at least one hit in two at-bats D) He gets EXACTLY one hit in two at-bats
13. When drawing from a standard deck of 52 cards without replacement, what is the probability of choosing: A) A face card followed by an ace B) Two consecutive cards of the same color
C) Three consecutive cards of the same suit D) Three cards, all of different suits
E) A black card or a king F) A heart or a 4 G) A king or a queen followed by a black jack
14.) Last season the Bengals passed on first down 40% of the time (and ran the ball 60% of the time). If they passed on first down, the probability they passed on second down was 30%. If they selected a running play on first down, the probability they passed on second down was 80%. Find the probability the Bengals will:
A) pass on first and second down. B) pass on first down, but not second down C) pass on second down, but not on first down D) pass on neither first nor second down E) Add the four probabilities. How do you explain this result?
15.) A coin is flipped five times. What is the probability of flipping at least one tails?
16.) If a basketball player makes 60% of his free throws, what is probability that he makes EXACTLY 2 out of 3 shots?
R1.) The larger of two supplementary angles exceeds 7 times the smaller by 4º. What is the measure of the larger angle?
R2.) The measure of the supplement of an angle is 30º less than five times the measure of the complement. What is the measure of the angle?
Selected Solutions: 2 b) 2/7 8 d) 19/66 9 c) 7/34 f) 197/340 12. d) .4352 13.) 7/13 16.) .432