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Given info: A card is selected from a pack of cards and then it is replaced. This is done for five times. Calculation:

Given info: A card is selected from a pack of cards and then it is replaced. This is done for five times. Calculation:

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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Hi, Could you please help me understand how that 10 fits into the answer part of the equation. I do have 0.0156 and 0.5625 however I'm not sure how the number 10 occurs. Thank you.

 

Given info: A card is selected from a pack of cards and then it is replaced. This is done for five times. Calculation: Define the random variable x as the number of clubs. Also, the probability of getting a club in each selection is and there are two possible outcomes (selected card a club and selected card is not a club), and each selection is independent of the other. Hence, x follows binomial distribution The formula for the binomial distribution is, n! P(x) = (-x) x P²q-x Where, n is the number of trials, x is the number of successes among n trials, p is the probability of success and q is the probability of failure. Substitute n as 5, x as 3, p as 0.25 (= 12) and q as 0.75 (= 1 -0.25) The probability of getting exactly three clubs is calculated as follows: P (3) = 5! (5-3)!3! (0.25)³ (0.75)5-3 120 (0.0156) (0.563) (2)(6) (10) (0.0156) (0.563) ≈ 0.088 Thus, the probability of getting exactly three clubs is 0.088. = =
Transcribed Image Text:Given info: A card is selected from a pack of cards and then it is replaced. This is done for five times. Calculation: Define the random variable x as the number of clubs. Also, the probability of getting a club in each selection is and there are two possible outcomes (selected card a club and selected card is not a club), and each selection is independent of the other. Hence, x follows binomial distribution The formula for the binomial distribution is, n! P(x) = (-x) x P²q-x Where, n is the number of trials, x is the number of successes among n trials, p is the probability of success and q is the probability of failure. Substitute n as 5, x as 3, p as 0.25 (= 12) and q as 0.75 (= 1 -0.25) The probability of getting exactly three clubs is calculated as follows: P (3) = 5! (5-3)!3! (0.25)³ (0.75)5-3 120 (0.0156) (0.563) (2)(6) (10) (0.0156) (0.563) ≈ 0.088 Thus, the probability of getting exactly three clubs is 0.088. = =
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