What is the probability to obtain exactly 2 heads out of 3 tosses of a fair coin?

We will figure out the general question first: if we have n consecutive events with two possible outcomes which we will tell "successes" and "failures" with probabilities p and 1-p, respectively, we call they have a binomial distribution. Then, the chance to obtain exactly k successes out of the n trials is: (n chooses k)(p^k)(p-1)^(n-k). ( where (n chooses k) is the binomial coefficient ).
Applying this formula to our problem we have: success if we obtain heads with probability p=0.5 and a failure if we obtain tails with probability 1-p=0.5, and we have n=3 trials at total and we ask the probability to obtain 2 heads = 2 successes. ( the successes and failures depends on how we choose what we will call success and what failure. We have to give them the right corresponding probabilities and trial )
Then we obtain the following expression: (3 chooses 2)(0.5^2)(0.5^1)=3*0.125=0.375

Answered by Stamo G. Maths tutor

3131 Views

See similar Maths A Level tutors

Related Maths A Level answers

All answers ▸

Using answer to previous question state the coordinates of the minimum


How to perform integration by substitution. (e.g. Find the integral of (2x)/((4+(3(x^2)))^2)) (10 marks)


A curve has the equation, 6x^2 +3xy−y^2 +6=0 and passes through the point A (-5, 10). Find the equation of the normal to the curve at A.


The curve C has equation y = x^3 - 3x^2 - 9x + 14. Find the co-ordinates and nature of each of the stationery points of C.


We're here to help

contact us iconContact usWhatsapp logoMessage us on Whatsapptelephone icon+44 (0) 203 773 6020
Facebook logoInstagram logoLinkedIn logo
Cookie Preferences