Answer:
A) 0.1855
B) 0.0010376
C) 0.0001297
D) 0.006363
E) 0.000007629
Explanation:
In calculation of a probability, we normally take the ratio of the number of ways to meet a certain condition (i.e. the numerator) divided by the number of ways to pick from a pool (i.e. the denominator).
So what are the number of ways the flip of a coin 17 times can come out?
A coin has a head and tail, so each toss will have two possible results. If we toss once, we have 2 possible results. If we toss, twice we have 2² = 4 possible results.
If we toss thrice, we have 2³ = 8 possible results, etc.
Thus, for 17 tosses, we will have 2^(17) = 131072 possible results.
A) To achieve the probability of getting 9 heads, we will use combination formula;
C(n, k) = n! / (k!(n - k)!)
In this case, n = 17 and k = 9
So,
P(9 heads) = 17! / (9!(17 - 9)!) = 24310
Thus,
P(9 heads in 17 tosses of a fair coin) = 24310/131072 = 0.1855
B) Similar to A above;
P(2 heads) = 17! / (2!(17 - 2)!) = 136
Thus,
P(2 heads in 17 tosses of a fair coin) = 136/131072 = 0.0010376
C) Similar to A above;
P(1 tail) = 17! / (1!(17 - 1)!) = 17
Thus,
P(1 tail in 17 tosses of a fair coin) = 17/131072 = 0.0001297
D) probability of getting 14 or more heads?
Since, there are 17 tosses, this will be;
P(14 or more heads in 17 tosses) = P(14 heads in 17 tosses) + P(15 heads in 17 tosses) + P(16 heads in 17 tosses) + P(17 heads in 17 tosses)
P(14 heads) = 17! / (14!(17 - 14)!) = 680
P(15 heads) = 17! / (15!(17 - 15)!) = 136
P(16 heads) = 17! / (16!(17 - 16)!) = 17
P(17 heads) = 17! / (1!(17 - 17)!) = 1
Thus;
P(14 heads in 17 tosses) = 680/131072 = 0.005188
P(15 heads in 17 tosses) = 136/131072 = 0.0010376
P(16 heads in 17 tosses) = 17/131072 = 0.0001297
P(1 head in 17 tosses) = 1/131072 = 0.00000763
P(14 or more heads in 17 tosses) = 0.005188 + 0.0010376 + 0.0001297 + 0.00000763 = 0.006363
E) Similar to A above;
P(17 tails) = 17! / (17!(17 - 17)!) = 1
Thus,
P(17 tails in 17 tosses of a fair coin) = 1/131072 = 0.000007629