Consider an experiment where a fair coin is tossed N times. There is a natural o
ID: 3322790 • Letter: C
Question
Consider an experiment where a fair coin is tossed N times. There is a natural outcome space for the experiment of tossing coins in sequence, where the probability of each outcome is equally likely. For example, if you toss 2 coins, the outcome space is {{H,H}, {H, T}, {T, H}, {T,T}}. The size of this outcome space is 4 and the probability of getting each outcome is 1/4.
Suppose a fair coin is tossed 9 times.
1) What is the size of the event set for getting exactly 8 heads?
2) What is the probability of getting exactly 8 heads?
3) What is the probability of getting at most 8 heads?
Explanation / Answer
1) Since there are 9 tosses and 8 turn heads only one of them turns tails and this can be any of the 9 tosses. Thus the size of the event set is 9.
2) The one tails can come in 9 ways and the probability of both the heads and tails is 1/2 or 0.5.
=> Probability of getting exactly 8 heads = 9 * 0.58 * 0.5 = 9 * 0.59 = 0.017578125.
3) The probability of getting all 9 heads = 0.59 = 0.001953125.
=> The probability of getting atmost 8 heads = 1 - 0.59 = 0.998046875.