Answer:
In simplified fraction, it is expressed as : 1/16, 1/4, 3/8, 1/4, 1/16.
Step-by-step explanation:
The discrete probability distribution for the random variable is as follows:
The number of tails possible in four tosses of a coin are 0,1,2,3,4
The total number of outcomes are
The Probability distribution is
X 0 1 2 3 4
P(X) 1/16 4/16 6/16 4/16 1/16
Therefore, In simplified fraction, it is expressed as : 1/16, 1/4, 3/8, 1/4, 1/16.
The discrete probability distribution table for the outcome of tails obtainable from 4 coin tosses :
Sample space for 4 coin tosess:
{HHHH, HHHT, HHHT, HHTT, HTHH, HTHT, HTHT, HTTT, THHH, THHT, THHT, THTT, TTHH, TTHT, TTHT, TTTT}
Recall :
[tex] probability = \frac{required \: outcome}{total \: possible \: outcomes} [/tex]
Possible Number of tails are 0, 1, 2, 3 and 4
For 0 tail :
P(0T) = [tex] \frac{1}{16} [/tex]
For 1 tail :
P(1T) = [tex] \frac{4}{16} = \frac{1}{4}[/tex]
For 2 tails :
P(2T) = [tex] \frac{6}{16} = \frac{3}{8}[/tex]
For 3 tails :
P(3T) = [tex] \frac{4}{16} = \frac{1}{4}[/tex]
For 4 tails :
P(4T) = [tex] \frac{1}{16}[/tex]
Therefore, the discrete probability distribution table is displayed thus :
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