in 6 bernoulli trials with probability P for success the pro

in 6 bernoulli trials with probability P for success, the probability of 2 successes = the probability of 3 successes. Find the P value . Show work

Solution

Given, total no of Bernoulli trial is 6 (n=6)

pmf of bernoulli distribution is P(X=x)= nc_xP^xq^n-x

Given P(x=2) = P(x=3)

(6c₂P²q^6-2)=( 6c₃P³q^6-3)

15* P²q⁴ =20* P³q³

15*q=20*P

15(1-P)=20*P

15-15P=20P

35P=15

P=15/35

P=0.428571