A person predicts daily whether the price of stocks of wrist watch companies will go up or down. If his prediction on stock price of Titan is correct 4 times out of 8, for Rolex it is correct 2 times out of 4 and for Fossil it is correct 2 times out of 9, then what is the probability that at least two of his predictions are correct on a given day?

Probability that price of titan is correct $P_1=\dfrac{4}{8}=0.5$

Probability that price of Rolex is correct $P_2=\dfrac{2}{4}=0.5$

Probability that price of Fossil is correct $P_3=\dfrac{2}{9}=0.22$

Probability that at least two of his predictions are correct on a given day

$=P_1P_2\bar{P_3}+P_1\bar{P_2}P_3+\bar{P_1}P_2P_3+P_1P_2P_3\\=(0.5)(0.5)(1-0.22)+(0.5)(1-0.5)(0.22)+(1-0.5)(0.5)(0.22)+(0.5)(0.5)(0.22)\\=0.195+0.055+0.055+0.055\\=0.36$