There are 21 plates of tomato sandwiches, 27 plates of cheese sandwiches, and 12 plates of beef sandwiches on a buffet table.

if a guest randomly picks a single plate, what is the probability that he gets tomato or cheese sandwiches?

show your work.

A3cm×3cm\greend{3\,\text{cm} \times 3\,\text{cm}} 3cm×3cm start color greend, 3, space, c, m, times, 3, space, c, m, end color greend rectangle sits inside a circle with radius of 4cm\blued{4\,\text{cm}} 4cm start color blued, 4, space, c, m, end color blued . what is the area of the shaded region? round your final answer to the nearest hundredth.