- null - Bernoulli Trials and Binomial Distribution
Suppose X has a binomial distribution `B(6, 1/2)`. Show that X = 3 is the most likely outcome.
(Hint: P(X = 3) is the maximum among all P (xi), xi = 0, 1, 2, 3, 4, 5, 6)
There are 5% defective items in a large bulk of items. What is the probability that a sample of 10 items will include not more than one defective item?
A couple has two children, Find the probability that both children are males, if it is known that at least one of the children is male.
A couple has two children, Find the probability that both children are females, if it is known that the elder child is a female.
An experiment succeeds twice as often as it fails. Find the probability that in the next six trials, there will be at least 4 successes.
Five cards are drawn successively with replacement from a well-shuffled deck of 52 cards. What is the probability that
(i) all the five cards are spades?
(ii) only 3 cards are spades?
(iii) none is a spade?