Answer:
0.84306608
Explanation:
The probability of an event, e, occurring exactly r times over n trials follows the formula
(n combination r) * p^r * q ^ (n-r)
with p being the probability the event will occur and q being the probability the event will not occur.
I assume you have a calculator/can find one online that can do combinations.
Here, we want to figure out if you get:
- 0 tails
- 1 tail
- 2 tails
If you get 3 or 4 tails, we are getting more than the 2 tails desired
For 0 tails:
- p is the probability a tail will occur = 0.38
- we want it to occur 0 times, so r = 0
- q is (1-p) = 1- 0.38 = 0.62
- we have 4 trials, as we flip it 4 times
(n combination r) * p^r * q ^ (n-r) = (4 combination 0) * (0.38) ^0 * (0.62) ^(4-0) = 1 * (0.38) ^0 * (0.62) ^(4-0) = 0.14776336
For 1 tail:
- p = 0.38, q = 0.62 as with 0 tails
- r = 1, n = 4
(n combination r) * p^r * q ^ (n-r) = (4 combination 1) * (0.38) ^1 * (0.62) ^(4-1) = 4* (0.38) ^1 * (0.62) ^(4-1) = 0.36225856
For 2 tails:
- p = 0.38, q = 0.62 as with 0 tails
- r = 2, n = 4
(n combination r) * p^r * q ^ (n-r) = (4 combination 2) * (0.38) ^1 * (0.62) ^(4-2) = 6* (0.38) ^2 * (0.62) ^(4-2) = 0.33304416
add our 3 probabilities together
0.33304416 + 0.36225856 + 0.14776336 = 0.84306608 as our answer