Question

Problem 2 Suppose you flip a penny and a dime. Each coin is equally likely to come up heads and tails. The two flips are independent a) What is the sample space? b) What is the conditional probability that both coins come up heads, given that the penny comes up heads? c) What is the conditional probability that both coins come up heads, given that at least one of the coins comes up heads? (Hint: the answers in part (b) and (c) should not be the same.)

Answer 1

A)HERE WE HAVE POSSIBLE RESULTS.

PENNY	DIME
H	T
H	H
T	H
T	T

SAMPLE SPACE={(H,T)(H,H)(T,H)(T,T)}

========================================================================

B)HERE THERE ARE TWO WAYS IN WHICH PENNY COMES UP HEADS,AND ONLY ONE WAY IN WHICH BOTH THE COINS HAVE HEADS.

SO PROBABILITY =1/2

============================================================================C)HERE EXCEPT THE (T,T) CASE ALL THE CASES HAVE ATLEAST ONE HEAD AND THERE IS ONLY ONE CASE IN WHICH BOTH THE COINS HAVE HEADS.

SO PROBABILITY=1/3