8 coins are tossed simultaneously, find the chance of obtaining at least six heads

37/256

Step-by-step explanation:

We need to use the Binomial distribution here, ask me why?

because there are only two outcomes of the experiment, heads or tails, which are complementary by nature, that is to say they are mutually exclusive and if one doesn't happen the other definitely does

p(head)+p(tail) = 1

also the trials are independent of one another, that is to say that the outcome of one toss doesn't affect the outcome of any of the other seven tosses out of 8.

and I am assuming here that the coins are all unbiased, i.e. p(head)=p(tail)=0.50

Considering all of these the possibility that we will get at least 6 heads out of 8 tosses is given by

p(head=6)+p(head=7)+p(head=8)= 8C6 (0.5)^6 (0.5)^2 + 8C7 (0.5)^7 (0.5)^1 + 8C8 (0.5) ^8

The plus sign indicates OR operator, i.e. we might get 6 heads or 7 heads or 8 heads.

where the probability mass function of the bin distn is given by

nCx p^x q^(n-x)

n= total number of trials

x= no. of success (in our case no of heads)

n-x = no of failures (no of tails in this example)

p= probability of success (p(heads)=0.5)

q= probability of failure (is equivalent of 1-p)

hey! so 1 (25) out of 4 (100) is 25 so your answer is 25%. it's like quarters!