Answer: 0.5
Step-by-step explanation:
Formula for binomial probability :-
[tex]P(x)=^nC_xp^x(1-p)^{n-x}[/tex], where P(x) is the probability of getting success in x trials , n is the total number of trials and p is the probability of getting success in each trial.
Given : The number of trails : n=7
The probability of success for each trial : p=0.5
Now, the probability that the number x of correct answers is fewer than 4 will be :-
[tex]P(x<4)=P(0)+P(1)+P(2)+P(3)\\\\=^7C_0(0.5)^0(0.5)^{7}+^7C_1(0.5)^1(0.5)^{6}+^7C_2(0.5)^2(0.5)^{5}+^7C_3(0.5)^3(0.5)^{4}\\\\=(0.5)^7+7(0.5)^7+21(0.5)^7+35(0.5)^7\\\\=(0.5)^7(64)=0.5[/tex]
Hence, the probability that the number x of correct answers is fewer than 4 = 0.5
