It was stated that a wrong answer costs a quarter point, so the expected value is 1(1/3) - (1/4)(2/3) = 1⁄6. A cost of 1⁄4 point for a wrong answer is too low though, since in that case the expected value of guessing from all four choices is still 1⁄16. The cost should be 1⁄3 to make that expectation equal 0.
It was stated that a wrong answer costs a quarter point, so the expected value is 1(1/3) - (1/4)(2/3) = 1⁄6. A cost of 1⁄4 point for a wrong answer is too low though, since in that case the expected value of guessing from all four choices is still 1⁄16. The cost should be 1⁄3 to make that expectation equal 0.