The probability distribution for the number of heads occurring in three coin tosses is given below and this can be determined by using the formula of the probability distribution.
Given :
- The sample space, S, of a coin being tossed three times is shown below, where Hand T denote the coin landing on heads and tails respectively.
- S = {HHH, HHT, HTH, HTT, THH, THT, TTH, TTT}
- Let X = the number of times the coin comes up heads.
The following steps can be used in order to determine the probability distribution for the number of heads occurring in three coin tosses:
Step 1 - The formula of the probability distribution is given below:
[tex]\rm P(X_i) = \dfrac{n(X_i)}{n(S)}[/tex]
where [tex]X_i[/tex] is the probability, [tex]\rm n(X_i)[/tex] is the expected outcome, and n(S) is the total outcome.
Step 2 - The probability that the head comes three times in the first throw is given by:
[tex]\rm P(X_1)=\dfrac{3}{3}[/tex]
Step 3 - The probability that the head comes 2 times in the 2nd, 3rd, and in the 5th throw is given by:
[tex]\rm P(X_2)=\dfrac{2}{3}[/tex]
[tex]\rm P(X_3)=\dfrac{2}{3}[/tex]
[tex]\rm P(X_5)=\dfrac{2}{3}[/tex]
Step 4 - The probability that the head comes 1 time in the 4th, 6th, and in the 7th throw is given by:
[tex]\rm P(X_4)=\dfrac{1}{3}[/tex]
[tex]\rm P(X_6)=\dfrac{2}{3}[/tex]
[tex]\rm P(X_7)=\dfrac{2}{3}[/tex]
Step 5 - The probability that no head comes in the 8th throw is given by:
[tex]\rm P(X_8)=0[/tex]
Therefore, the correct option is B).
For more information, refer to the link given below:
https://brainly.com/question/795909
