Question

A fair coin is tossed 29 times. In how many outcomes do at least 2 tails occur?

a. 536,870,476
b. 1
c. 536,870,883
d. 536,870,882
e. 406
f. None of the above

Answer 1

To find the number of outcomes where at least 2 tails occur when a fair coin is tossed 29 times, the total number of outcomes (2²⁹) is subtracted by the number of outcomes with fewer than 2 tails.

Step-by-step explanation:

To find the number of outcomes where at least 2 tails occur when a fair coin is tossed 29 times, we can use the complement rule. First, let's find the number of outcomes where fewer than 2 tails occur.

We can consider the number of tails as 0 or 1. There are 30 possible outcomes with 0 tails (all heads), and 29 possible outcomes with 1 tail. So, the number of outcomes with at least 2 tails would be the total number of outcomes (2²⁹) minus the number of outcomes with fewer than 2 tails.

Number of outcomes with fewer than 2 tails: 30 + 29 = 59

Number of outcomes with at least 2 tails: 2²⁹ - 59 = 536,870,883. Therefore, the correct answer is c. 536,870,883.

Answer 2

d. 536,870,882

Step-by-step explanation:

The number of outcomes in which at least 2 tails occur (N(t>1)) is given by the total number of possible outcomes (N) subtracted by the number of possibilities in which one or none tails occur.

For each throw, there are two possible outcomes. The total number of outcomes is:

`N= 2^(29)\\N=536,870,912`

There is only one outcome where no tails occur, while there 29 outcomes in which only one tails occur (one for each toss).

Therefore, the number of outcomes in which at least 2 tails occur is:

`N(t>1) = 536,870,912 - 29 -1\\N(t>1) = 536,870,882`

d. 536,870,882