A fair die is toss six times. Defined a random variable as an odd number that appeared. Find the probability that exactly four of the tosses showed an odd number.

Answer 1

prob (odd on a single toss) = 3/6 = 1/2
prob(not odd) = 1/2

prob that of 6 tosses, exactly 4 will show an odd
= C(6,4) (1/2)^4 (1/2)^2
= 15(1/2)^6
= 15/64

Answer 2

A poker hand is a hand made of five cards chosen from a standard deck of cards. Suppose a random
variable J gives the number of hearths in the hand.
a. P(J=0)
b. P(J=1)
c. P(J=2)
d. P(J=3)
e. P(J=4)
f. P(J=5)
g. Construct the probability mass function and its corresponding histogram.