Binomial Probability

BINOMIAL PROBABILITY 

Binomial probability refers to the probability of exactly x successes on n repeated trials in an experiment which has two possible outcomes (commonly called a binomial experiment).

If the probability of success on an individual trial is p , then the binomial probability is 

               C(n,x)pˣ(1-k)ⁿ⁻ᵏ

Q)A multiple choice examination has 7 questions each question has 4 alternative answers of which only one is correct the probability that the student will get 4 correct answer just by guessing is 

Answer:-945/(4⁷)

Solution 

P(getting correct answer)=1/4

using Binomial probability

C(7,4)(1/4)⁴(3/4)³ = 945/4⁷

2)A coin comes up head with probability p greater than 0 and tail with probability (1-p) greater than 0 suppose the probability of 4 heads and 5 tail is equal to 1/3 the probability of getting 5 head and 4 tail find p

Answer = 3/4

Solution 

To solve this problem we need the knowledge of binomial probability

Our first aim is  to find the value of p using the given conditions 

Probability of getting 4 head 5 tail can be found out using Binomial probability

C(9,4)p⁴(1-p)⁵

Probability of getting 5 head 4 tail

Is C(9,5)p⁵(1-p)⁴

C(9,4)p⁴(1-p)⁵=1/3[C(9,5)p⁵(1-p)⁴]

3p⁴(1-p)⁵=p⁵(1-p)⁴

3(1-p)=p

p=3/4