How does experimental probability 43 out of 53 compare with theoretical probability 0.50?

Answer 1

43/53 = 0.81 : This is not even close to the theoretical probability of 0.50 ; With 0.50, the expected outcome is 26.5 out of 53. I would expect not to get 26 or 27, though - but a range from 21 to 33 (out of 53) would be in my expectations.

Imagine coin tosses (probability = 0.5): it is possible to get 43 out of 53, but the chance of this happening is very very small. I don't remember the exact formulas, but consider this: flip a coin 5 times. There are 32 possible outcomes. Only 6 of these 32 would give a 1 out of 5 (or less). This is 6/32 or about 19%. So to get 40 (or more) out of 50, you would need to get 4 (or more) out of 5, ten times, or (6/32)^10 = about 1 in 18 million. To get 43 (or more) out of 53 would be even a smaller chance than this. This is on the scale of chances of winning the lotto (definitely possible, but not probable).