Four coins are tossed. Let Z be the random variable representing the number of the heads that occur. Construct a table of the possible outcomes with corresponding values of the random variable.
Four coins are tossed. Therefore sample space contain "2^4" i.e "16" points.
Let "S" be the sample space.
Then "S=" { "HHHH,HHHT,HHTH,HHTT,HTHH,HTHT,HTTH,HTTT"
"THHH,THHT,THTH,THTT,TTHH,TTHT,TTTH,TTTT" }
Let "Z" be the random variable representing the number of heads that occur.
Then "Z" can take the values "0,1,2,3,4."
Now corresponding to each points of random variable "Z" we will get their probabilities.
"\\therefore P(Z=0)=" probability of getting no head
"=\\frac{1}{16}"
"P(Z=1)=" probability of getting one head
"=\\frac{4}{16}=\\frac{1}{4}"
"P(Z=2)=" probability of getting two head
"=\\frac{6}{16}=\\frac{3}{8}"
"P(Z=3)=" probability of getting three head
"=\\frac{4}{16}=\\frac{1}{4}"
"P(Z=4)=" probability of getting four head
"=\\frac{1}{16}"
Which are the required values of random variable "Z."
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