# Hotmath

Title:
Hotmath
Author:
Hotmath
Chapter: Sequences and Series Section: Binomial Probability and Binomial Distribution

Problem: 1

You guess the answers to 6 questions on a multiple–choice test with 5 possible responses to each question. Describe a trial and a success for the above situation. Find the number of trials. Find the probability of answering 4 questions correctly.

Problem: 3

You guess on a true/false test. Find P (1 correct in 5 guesses).

Problem: 5

You guess on a true/false test. Find P (3 correct in 5 guesses).

Problem: 7

Find the probability of tossing a fair coin 20 times and getting 2 heads.

Problem: 9

Find the probability of tossing a fair coin 20 times and getting 12 heads.

Problem: 11

There are 40 questions for which there are 4 choices for each. Find the probability of randomly guessing 2 correct answers out of it.

Problem: 13

There are 40 questions for which there are 4 choices for each. Find the probability of randomly guessing 20 correct answers out of it.

Problem: 15

The probability of getting tails when tossing a biased coin is 60%. If you toss the coin 3 times, what is the probability of getting 2 tails and 1 head?

Problem: 17

Find the probability of 3 successes in 6 trials, if the probability of success is 0.4.

Problem: 19

Find the probability of 6 successes in 12 trials, if the probability of success is 0.2.

Problem: 21

Find the probability of having not more than 2 successes in 4 trials, if the probability of success is 0.4.

Problem: 23

Find the probability of having not more than 5 successes in 10 trials, if the probability of success is 0.75.

Problem: 25

Draw a histogram of the binomial distribution that shows the probability of exactly k successes for a binomial experiment which consists of 5 trials with probability 0.6 of success on each trial. Also find the most likely number of successes.

Problem: 27

Draw a histogram of the binomial distribution that shows the probability of exactly k successes for a binomial experiment which consists of 10 trials with probability 0.077 of success on each trial. Also find the most likely number of successes.

n = 10

p = 0.077

Problem: 29

In a school exam, one student out of 80 fails. Determine the probability that out of 20 students picked at random, exactly 1 student fails.

Problem: 31

A cat gives birth to a litter of 9 kittens. Find the probability of having at least 6 female kittens assuming that the probability of a kitten being female is 0.7.