Question

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.

Answer 1

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 $Z.$