Statistics: Math Help - Binomial Distribution

Question

A fair coin is flipped 13 times. Find the probability that more than 7 of the flips turn up tails.

1. __0.290527
2. __0.265906
3. ❌0.242364
4. __0.316153
5. __0.342697
6. __0.178765

Answer 1

Probability of 7 or more = the Probability of 6 or less tails, if flipped 13 times

1 way to get zero tails in 13 flips, 13C0 = 1 = 1 way to get 13 tails

13 ways to get 1 tail, 13C1 = 13 = 13 ways to get 12 tails

2 tails, 13C2 = 13x12/2 = 78 ways to get 2 tails or get 11 tails

3 tails, 13C3 = 13x12x11/3x2 = 276 ways to get 3 tails or 10 tails

4 tails 13C4 = 13x12x11x10/4x3x2 = 715 ways to get 4 tails or 9 tails

5 tails, 13C5 = 13x12x11x10x9/5x4x3x2 = 1287 ways to get 5 tails or 8 tails

6 tails 13C6 = 13x12x11x10x9x8/6x5x4x3x2 = 13x12x11=1716 ways to get 6 tails or 7 tails

ways to get 7 or more = 1716 +1287+715+276+78+13+1 = 3003+991+92= 4086 = ways to get 6 or less

total ways = 8172

P(7 or more) = P(6 or less) = 1/2

P(more than 7) = (4086-1716)/8172 =2370/8172 = about 0.290

best answer is the 1st choice

you can read the same number of ways or 13Cn off the 13th row of Pascal's Triangle