Question

Assume that there are 2 trials. X = 2 where X represents the number of successes. Which probability matches the probability histogram? Round the answer to one decimal place. P(success)=0.2 P(success)=0.4 P(success)=0.6 P(success)=0.8

Answer 1

Answer is P(success) is `0.6`.

Explanation:

In a binomial distribution probability, if probability of a success is `p` and that offailure is `q` (note that `q=1-p`), then probability of `x` successes out of `n` trials is `C_x^np^xq^(n-x)`

Now if their are two trials

probability of `0` success is `C_0^2p^0q^2=q^2`

probability of `1` success is `C_1^2p^1q^1=2pq` and

probability of `2` success is `C_2^2p^2q^0=p^2`

Now see the graph. As `q^2=0.16`, we have `q=0.4` and as `p^2=0.36` we have `p=0.6`

Of course then `2pq=0.48`

Hence, answer is P(success) is `0.6`.