Binomial probabilities

Answer Key - Grade 11 Math Worksheet - Challenge Me

Circle the best answer, or write your answer on the line.

1. 1.

   Outcome list: each try is counted (0.5) or not (0.5). Noah tosses a fair coin 6 times. To the nearest thousandth, what is the chance of at least 5 heads?

   0.109
2. 2.

   Outcome list: each try is counted (0.3) or not (0.7). Pia checks 4 phone cases, and each has a scratch with chance 0.3. To the nearest thousandth, what is the chance of at most 1 scratched case?

   0.652
3. 3.

   A binomial count needs a fixed number of tries, two outcomes, and the same chance each time. Which situation of Tala's fits a binomial distribution?

   • Tala shoots 10 free throws, each made with chance 0.7; X counts the makes
   • Tala rolls a fair number cube once; X is the number it shows
   • Tala picks 3 cards at random from 10 cards, 4 red, without putting any back; X counts the red cards
   • Tala tosses a fair coin until it lands heads; X counts the tosses
4. 4.

   A binomial count needs a fixed number of tries, two outcomes, and the same chance each time. Which situation of Zee's fits a binomial distribution?

   • Zee measures the heights of 8 plants; X is the tallest height
   • Zee guesses on 8 quiz questions, each with 4 choices; X counts the right guesses
   • Zee takes 2 pens at random from a cup of 6, 2 blue, without putting them back; X counts the blue pens
   • Zee spins a spinner until it lands on red; X counts the spins
5. 5.

   A binomial count needs a fixed number of tries, two outcomes, and the same chance each time. Which situation of Bo's fits a binomial distribution?

   • Bo plants seeds one by one until one sprouts; X counts the seeds planted
   • Bo picks 4 names at random from a list of 12, 5 from one class, with no name picked twice; X counts that class's names
   • Bo plants 12 seeds, each sprouting with chance 0.8 on its own; X counts the sprouts
   • Bo counts the leaves on one plant; X is that count
6. 6.

   A binomial count needs a fixed number of tries, two outcomes, and the same chance each time. Which situation of Esme's fits a binomial distribution?

   • Esme tosses a fair coin until 2 heads in a row land; X counts the tosses
   • Esme tosses a fair coin 20 times; X counts the heads
   • Esme picks 5 cubes at random from a bag of 10, 3 green, without putting any back; X counts the green cubes
   • Esme times one walk to school; X is the minutes
7. 7.

   Each try is counted (0.3) or not (0.7). Jun makes each free throw with chance 0.3. What is the fewest shots for a chance of at least 0.9 of getting at least 1 make?

   7
8. 8.

   Each try is counted (0.2) or not (0.8). Each seed in Kira's old seed packet sprouts with chance 0.2. What is the fewest seeds for a chance of at least 0.95 of getting at least 1 sprout?

   14
9. 9.

   Each try is counted (0.1) or not (0.9). Each of Luz's long bean-bag throws lands in the basket with chance 0.1. What is the fewest throws for a chance of at least 0.5 of getting at least 1 hit?

   7
10. 10.

    Each try is counted (0.4) or not (0.6). Each of Milo's paper airplanes lands in the hoop with chance 0.4. What is the fewest throws for a chance of at least 0.99 of getting at least 1 landing?

    10