Question

Assume that random guesses are made for seven multiple choice questions on an SAT​ test, so that there are equals 7 ​trials, each with probability of success​ (correct) given by pequals0.5. Find the indicated probability for the number of correct answers. Find the probability that the number x of correct answers is fewer than 4.

Answer 1

3 are fewer

Explanation:

Answer 2

Answer: 0.5

Explanation:

Formula for binomial probability :-

`P(x)=^nC_xp^x(1-p)^(n-x)`, 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 :-

`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`

Hence, the probability that the number x of correct answers is fewer than 4 = 0.5