Ex 7.2, 3 - Chapter 7 - The Mathematics of Maybe: Introduction to Probability

Transcript

Ex 7.2, 3 (i) Toss a coin 20 times and record the result each time (heads or tails). (i) How many times did you get heads? Let's pretend I flipped a coin 20 times and got Heads 12 times and Tails 8 times Now, We got Heads 12 times Ex 7.2, 3 (ii) Toss a coin 20 times and record the result each time (heads or tails). (ii) How many times did you get tails? We got Tails 8 times Ex 7.2, 3 (iii) Toss a coin 20 times and record the result each time (heads or tails). (iii) Calculate the experimental probability of getting heads. Now, Experimental probability of getting heads = (𝑵𝒖𝒎𝒃𝒆𝒓 𝒐𝒇 𝒕𝒊𝒎𝒆𝒔 𝒘𝒆 𝒈𝒆𝒕 𝑯𝒆𝒂𝒅𝒔)/(𝑻𝒐𝒕𝒂𝒍 𝒏𝒖𝒎𝒃𝒆𝒓 𝒐𝒇 𝑪𝒐𝒊𝒏 𝒕𝒐𝒔𝒔) = 12/20 = 3/5 = 0.6 = 60% Ex 7.2, 3 (iv) Toss a coin 20 times and record the result each time (heads or tails). (iv) If you toss the coin once more, what is the probability of getting tails? The probability is exactly 𝟏/𝟐 (or 𝟓𝟎% ). This is because of Gambler's Fallacy It does not matter what happened in your 20 previous experimental tosses. The 21st toss is a brand new, independent event, and a fair coin always has a theoretical probability of 𝟏/𝟐 for Tails.