# Using the Probability Mass Function Over a Range

How do i calculate P(X=1)+P(X=2)+P(X=3) individually to get the results 0.1562+0.3125+0.3125 ? Could be pretty simple but im kinda stuck

No one answered user bonoboboc, so I thought I’d create a new thread.
Forums: FAQ: Introduction to Probability Distributions - Using the Probability Mass Function Over a Range

We are tossing a coin `5` times.

There are a total of 25 or `32` outcomes (e.g. if `T` denotes a tail and `H` denotes a head, then the sample space will have `32` possibilities: `TTTTT, HTTTT, THTTT, ..., THHHH, HHHHH`)

`0` heads —>   5C0 —> 1 outcome

Probability of `0` heads = 132 = `0.03125`

`1` heads —>   5C1 —> 5 outcomes

Probability of `1` heads = 532 = `0.15625`

`2` heads —>   5C2 —> 10 outcomes

Probability of `2` heads = 1032 = `0.3125`

`3` heads —>   5C3 —> 10 outcomes

Probability of `3` heads = 1032 = `0.3125`

`4` heads —>   5C4 —> 5 outcomes

Probability of `4` heads = 532 = `0.15625`

`5` heads —>   5C5 —> 1 outcome

Probability of `5` heads = 132 = `0.03125`

(Check)
Sum of probabilities of all outcomes = `0.03125 + 0.15625 + 0.3125 + 0.3125 + 0.15625 + 0.03125 = 1`

Probability of getting 1 to 3 heads = (Probability of 1 head) + (Probability of 2 heads) + (Probability of 3 heads) = `0.15625 + 0.3125 + 0.3125` = `0.78125`