SOLVED:You flip a coin 5 times that has been weighted such that heads come up twice as often as tails. What is the probability that all 5 of them are heads?

Video Transcript

the objective of this trouble is to calculate the probability of getting less than two heads. Given that a fair coin has been flipped five times. Okay, Since the fair mint has been flipped five times and we need to calculate the probability of getting hurt. So if I ask about what is the probability of getting head ? So the probability of getting act which Is going to be close to 1/2 which is .5. And the probability of not getting hag which is do not take by Q is equal to one minus P. And this in turn equals to one subtraction 10.5 which is 0.5. Alright, nowadays, here we have been given that the mint has been flipped five times. So let ‘s just suppose the And which is our sample size. All correct. Which is our sample size is going to be near to five and here we are going to And here we are going to use the binomial distribution in order to solve our interrogate and why we are going to use the by normal distribution. It is because Our sample size five is fixed. And for each of the trial, which is for each of the pass the probability of getting head or getting tell, there is alone two outcomes possible. And in this case we use The probability distribution officiate Alright. sol here the P is basically which is .5 is basically the probability of achiever, probability of success. Alright. And Q will be the probability of failure. No, here we have been given back the we are going to use the binomial distribution. Therefore let us assume the random variable adam here and this random variable x denotes the number of the heads. This, you know the phone number of heads. so basically our random variable star X is following the binomial distribution With the rate of the sample size to be conclude to five. And the measure of the probability of success to be equals 2.5. Alright. And we have to calculate the probability we have to calculate the probability that the value of X which is basically the phone number of getting ache should be less than so. This is what we are supposed to calculate. So before calculating this, let me introduce you with the formula of the binomial distribution. then according to the binomial distribution formula, the probability that capital ten is going to be equals two little x is basically given by n C X. hera says the combination. Alright, time ‘s address to the ability X hera pays the probability of success times Q to the power and minus X. All right nowadays this probability which is the probability of excess ballast tank to. This should be caused to the probability that X should be close to zero. Plus the probability that X is going to be close to one. nowadays we have to calculate each of these probability individually and then we can calculate our ask answer. Alright, so the probability that X is going to be near to zero is given by. Since the value of the sample size nitrogen is five, See the value of X will be zero times 00.5 to the exponent zero Times .5 to the office 10 5 0, which is five Plus. The probability that X is going to be close to one is given by 57 times 0.5 to the power one times 10.5 to the power five minus one, which is four. immediately we are going to solve each of these terms and calculate our needed probability. Therefore we can say that our probability of getting less than two heads should be equals two bespeak 1875 and hence this is the adjust on.

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