Question

A person has agreed to participate in an extrasensory perception (ESP) experiment. He is asked to randomly pick two numbers between 1 and 6 (inclusive). In addition, the second number must be different from the first. Let H = event the first number picked is a 3. K = event the second number picked exceeds 4.

(a) Find P(H).

(b) Find P(K|H). Hint: given that the 1st number is 3, what numbers are left for the man to select from? (c) Find P(K & H). Hint: use the multiplication rule. Are these events independent?

(d) Find the probability that both numbers picked is less than 3. Hint: redefine H and K appropriately and follow the same pattern as parts (a)-(c). 

Answer 1

a)

$$P(H)=\dfrac{1}{6}$$

b)

$$P(K|H)=\dfrac{2}{5}$$

c)

$$P(KH)=\dfrac{1}{6}(\dfrac{2}{5})=\dfrac{1}{15}$$

d)

$$P(both<3)=\dfrac{2}{6}(\dfrac{1}{5})=\dfrac{1}{15}$$