We know that n=4 (there are 4 trials) and P(X=0)=‌
16
81
(the chance of getting zero successes is ‌
16
81
). In a binomial distribution, p is the chance of success each time, and q is the chance of failure. q=1−p. The formula to find the probability of getting k successes is: P(X=k)=‌nCkpkqn−k. Step 1: Find q P(X=0)=‌4C0p0q4 ‌4C0=1 and p0=1, so: P(X=0)=1⋅1⋅q4=q4 We know q4=‌
16
81
. To find q, take the fourth root of both sides: q=‌
2
3
because (‌
2
3
)4=‌
16
81
. Step 2: Find p Since q=‌
2
3
, p=1−‌
2
3
=‌
1
3
. Step 3: Find P(X=4) P(X=4) is the probability of getting 4 successes out of 4 tries. P(X=4)=‌4C4p4q0 ‌4C4=1 and q0=1, So: P(X=4)=1⋅(‌