Question

Find the probability that Javier volunteers for at least one event each month.

$P(x>0)=\_\_\_\_\_\_\_$

Short answer

The probability that Javier volunteers for at least one event each month.

$P(x>0)=0.95$

Step-by-step solution

Step 1 : Given Information

At community events, Javier volunteers. He only attends five events per month. He attends exactly five activities $35\%$of the time, four events $25\%$of the time, three events $20\%$of the time, two events $10\%$of the time, one event$5\%$of the time, and no events $5\%$of the time.

Calculation & Explanation

The probability that Javier attends at least one event every month is the probability that $X$takes the value $1$or more, as calculated using the probability table. It is the probability that $X$will take the value $1or2or3or4or5$in terms of notation. Probabilities may be calculated since these events are mutually exclusive.

That is $P(X>0)$is:

$P\left(1\right)+P\left(2\right)+P\left(3\right)+P\left(4\right)+P\left(5\right)=0.05+0.10+0.20+0.25+0.35=0.95$

Is also $P(X>0)$identical to $1-P(X=0)$. This is because $X$taking a value higher than zero is the inverse of $X$taking a value of$0.$The probability of an occurrence is equal to the probability of a complementary event multiplied by $1.$