John plays a roulette 5 times; each time betting on

Kye

Kye

Answered question

2021-09-19

John plays a roulette 5 times; each time betting on red. The probability of red is 1838=919. Let X be the number of wins. Find the expected value (mean) E{X}, the standard deviation, and P(X=2).

Answer & Explanation

estenutC

estenutC

Skilled2021-09-20Added 81 answers

Step 1
Given: John plays a roulette 5 times; each time betting on red. The probability of red is 1838=919.
Let X be the number of wins.
Number of times plays a roulette: n=5
Probability of red: p=9190.47
Since, all trials are independent and probability of red in each trials is same which is 0.47. Therefore ,
XB(n=5,p=0.47)
Binomial probability formula is written as:
P(X=x)=(beg{array}{c}nxend{array})px(1p)nx
Step 2
The mean of binomial distribution is :
E(X)=np
=5(0.47)
E(X)=2.35
The standard deviation of binomial distribution is:
SD(X)=np(1p)
=5(0.47)(10.47)
SD(X)=1.1160
Here, n=5,p=0.47 and X=2
Using binomial probability formula:
P(X=2)=(beg{array}{c}52end{array})(0.47)2(10.47)52
=10(0.2209)(0.1489)
P(X=2)=0.3289

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