Question

Based on a poll, 40% of adults believe in reincarnation. Assume that 8 adults are randomly selected, and find the indicated probability?

Answer 1

This is clearly a Binomial experiment because,

1) Number of adults = 8 is fixed.

i.e number of trials is fixed.

2) All the adults are identical and independent in the aspect of believing in reincarnation.

3) Considering an adult he or she either believes (success) or not(failure).

4) Probability of believing (probability of success)= 40%=0.4 is same for every adult.

Now let X be number of adults who believe in reincarnation out of 8 adults.

Actually in our problem,no probability is indicated to determine.

So for your better understanding I consider the following probabilities and calculate them.

P(X=3):

Formula: P(X=x)=ncx.p^x .q^n-x.

here n=8, x=3,p=0.4,q=1-0.4=0.6

so, P(X=3)=8c3.(0.4)^3(0.6)^8-3

=0.2787 answer.

P(X<3):

P(X<3)=8cx.(0.4)^x.(0.6)^8-x. where x takes 0,1,2,

=0.3154 Answer.

P(X>=3):

PX>=3)=8cx.(0.4)^x.(0.6)^8-x. Here x takes 3,4,5,6...... infinity.

=0.6846 answer.

Note:We can find the above probabilities using Binomial calculator easily.