How the price of an Option is affected by the probability of price movement ?

Take an example - Let's say that SBI trades at Rs 250. It is possible for its price to move up by 50% to Rs 280 in the next month. There are 25%, 25%, 20%, and 15% chances that the SBI stock will move to Rs. 290, Rs 300 and Rs. 310 within this month.

How much would you make if your call option had a strike price at Rs 300?

The contract would be worthless if the stock price was to end at Rs 280 or Rs 290, respectively. If the SBI price finishes at Rs. 310 or Rs. 320, you will gain Rs 10 and Rs 20, respectively. The expected return on your call would be:

(50%*0)+(30%*0)+(25%*0)+(20%*10)+(15%*20) = Rs 5

For this SBI option contract you would prefer to pay less than Rs 5, and the seller would prefer to make more than Rs 5.