Question

johnny has a 70% chance of passing a test. If johnny has 4 tests this year, what is the probability that johnny passes all of his tests?

Answer 1

To find the probability that Johnny passes all of his tests, we can multiply the probability of passing each individual test together. Since Johnny has a 70% chance of passing each test, the probability of passing all four tests is 0.7^4. Therefore, the probability that Johnny passes all of his tests is approximately 0.2401, or 24.01%.

Step-by-step explanation:

To find the probability that Johnny passes all of his tests, we can multiply the probability of passing each individual test together. Since Johnny has a 70% chance of passing each test, the probability of passing all four tests is 0.7 multiplied by itself four times (0.7^4).

Let's calculate:

Probability of passing all four tests = 0.7^4 = 0.2401

Therefore, the probability that Johnny passes all of his tests is approximately 0.2401, or 24.01%.

Answer 2

The probability that johnny passes all of his tests (4) is 24.01%

Step-by-step explanation:

Let's recall that the binomial distribution is defined completely by its two parameters, n (number of trials) and p (probability of success). In our question, n = 4 and p = 0.7.

Also let's recall that the formula for finding the probability of x exact number of successes in n trials is:

b (x; n, P) = nCx * Px * (1 – P)n – x

Where:

b = binomial probability

x = total number of “successes” (pass or fail, heads or tails etc.)

P = probability of a success on an individual trial

n = number of trials

Using the formula above, we can elaborate our binomial distribution table, as follows:

Binomial distribution (n=4, p=0.7)

x Pr[X = x]

0 0.0081 0.81%

1 0.0756 7.56%

2 0.2646 26.46%

3 0.4116 41.16%

4 0.2401 24.01%

Therefore, the probability that johnny passes all of his tests (4) is 24.01%