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Assume that random guesses are made for eight multiple choice questions on an SAT test, so that there are n= 8 trials, each with probability of success (correct) given by p=0.3. Find the indicated probability for the number of correct answers. Find the probability that the number x of correct answers is fewer than 4​

Respuesta :

Answer:

0.80589

Step-by-step explanation:

So all of the numbers of correct answers less than 4 are 0,1,2,3

We need to calculate the probability for each separately and then add them together.

To find the probability we have to first find the combination. We know that there’s n=8 trials and that p=0.3. So 1-0.3 gives us 0.7.

The combination formula is: ! / (!(−)!)

So the n would always =8, and the r would be 0,1,2,3. So you would have to calculate it for 0,1,2,3 Separately. This can be done by hand or you can use a simple combinations calculator online.

For 0;

The combination is 1,

1 x 0.3^0 x 0.7^8-0 =

0.057648

For 1;

The combination is 8,

8 x 0.3^1 x 0.7^8-1 =

0.19765

For 2;

The combination is 28

28 x 0.3^2 x 0.7^8-2 =

0.296475

For 3;

The combination is 56

56 x 0.3^3 x 0.7^8-3 =

0.254122

All that’s left is to add these four numbers;

0.057647 + 0.19765 + 0.296475 + 0.254122 = 0.80589

fichoh

Using the principle of binomial probability, the probability of correct answers fewer than 4 is : 0.8059

Recall the binomial probability formula :

P(x = x) = nCx * p^x * q^(n-x)

Where :

  • n = number of trials
  • x < 4
  • p = probability of success = 0.3
  • q = 1 - p = 1 - 0.3 = 0.7

P(x < 4) = P(x = 0) + P(x = 1) + P(x = 2) + P(x = 3)

Using a binomial probability calculator :

  • P(x = 0) = 0.0576
  • P(x = 1) = 0.19765
  • P(x = 2) = 0.29648
  • P(x = 3) = 0.25412

Therefore,

  • P(x < 4) = (0.0576+0.19765+0.2965+0.25412) = 0.8059

Learn more : https://brainly.com/question/12474772

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