Applying Probability to Make Informed Decisions

A company has 500 employees, and 60% of them have children. Suppose that we randomly select 4 of these employees.

Which of the following would find the probability that exactly 3 of the 4 employees selected have children?

• (0.60)³(0.40)

• (0.60)(0.40)³

• ⁴C₃(0.60)³(0.40)

• ⁴C₃(0.60)(0.40)³

• ⁵⁰⁰C₃(0.60)³(0.40)

A small college has 800 students,

10% of which are left-handed.

Suppose they take sample of 8 students.

Let L= the number of left-handed students in the sample.

Which of the following would find P(L=2)?

• (0.10)²(0.90)⁶

• (0.10)⁶(0.90)²

• ⁸C₂(0.10)²(0.90)⁶

• ⁸⁰⁰C₂(0.10)²(0.90)⁶

Tomer is playing a game that involves rolling 5 of 6-sided dice at once, and his goal is to roll the dice so exactly 4 of them land showing a "1".

Which of the following would find the probability that exactly 4 of the 5 dice land showing a "1"?

• (⅙)⁴₍⅚₎

• ⁶C₅(⅙)⁴₍⅚₎

• ⁶C₅(⅙)⁴₍⅚₎²

• ⁵C₄(⅙)⁴₍⅚₎

• ⁵C₄(⅙)⁴₍⅚₎²

Jamal gets ready for a basketball game by shooting 10 free-throws. Based on previous data, he has a 70% chance of making each free-throw. Assume that the results of each free-throw are independent.

Which of the following would find the probability

of Jamal making exactly 88 of 10 free-throws?

• ¹⁰C₇(0.7)⁷(0.3)³

• ¹⁰C₈(0.7)⁸(0.3)²

• ¹⁰C₈(0.7)²(0.3)⁸

• (0.7)⁸(0.3)²

You are playing against Miss Soldan in a student/faculty basketball game. You know she is terrible at free throws (she has an 8% accuracy rate), so you keep fouling her. If she attempts 18 free throws, what is the probability that she makes more than 3 of them?

• 0.05
• 0.95
• 0.17
• 0.83

The student who makes the morning announcements has the bad habit of saying “like” all the time. The chance that they say “like” in a sentence is 60%. You decide to keep a tally of how many times they say like. If they say 350 sentences this week, what is the probability that they will say “like” at least 200 times?

• 0.87
• 0.13
• 0.85
• 0.15

According to a recent survey, 15% of houses in America are haunted by a ghost. If your neighborhood has 40 houses, what is the probability that 5 or more of them are haunted?

• 0.74
• 0.26
• 0.57
• 0.43

You have decided to drop out of school and move to Vegas, where you will learn to count cards and get rich. If you draw 12 cards out of a deck (with replacement), what is the probability that you get at least 7 red cards?

• 0.39
• 0.61
• 0.19
• 0.81

You are bored in Miss Soldan’s class, so you pass the time by flipping a coin 100 times. What is the probability that you get more than 51 tails?

• 0.38
• 0.62
• 0.46
• 0.54

You trick Miss Soldan into playing for the juniors in the Powder Puff football game. As a quarterback, she typically completes 3% of her passes. If she makes 25 passes in the game, what is the probability that she will complete at least 3?

• 0.04
• 0.96
• 0.01
• 0.99