Question

A fair coin is flipped 7 times. What is the probability that exactly 4 of the 7 flips come up heads? You may enter your answer as a fraction, an expression, or as a decimal rounded to at least 4 decimal places of precision. (e.g. if the probability were 3/9, you could enter 3/9 or 0.3333)

Answer 1

1. A coin is flipped 7 times.

No of ways in which 4 of these 7 flips are head = $\small _{4}^{7}\textrm{C}$ .

Probability of each head = 0.5

Probability of each tail = 0.5

Therefore, Probability that exactly 4 out of 7 are head =   $\small _{n}^{7}\textrm{C}$ * 0.5ⁿ * 0.5^(7-n)

⁼ $\small _{4}^{7}\textrm{C}$ * 0.5⁴ * 0.5^(7-4) = $\small _{4}^{7}\textrm{C}$ * 0.5⁴ * 0.5³  = 0.273438

2. A 20 sided dice is rolled. The numbers on the face are from 1 to 20.

The size of the sample space, when the dice is rolled once = 20 ( 20 possible outcomes are possible).

The size of the set that corresponds to the event that dice roll is odd = 10 ( the odd outcomes in this event are {1,3, 5, 7, 9, 11, 13, 15, 17,19}.

The probability that all dice rolled are odd = 10/20 =0.5.