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?

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%