Two fair dice are rolled 5 times. Let the random variable x represent the number of times that the sum 4 occurs. The table below describes the probability distribution. Find the value of the missing probability.
x P(x)
0 0.64722784850823
1 0.29419447659465
2 0.0534899048353909
3
4 0.000221032664609053
5 4.01877572016461e-06
sum the given probabilities and subtract from 1
To find the missing probability, we can use the fact that the sum of probabilities for all possible values of x must equal 1.
So, we need to find the missing probability such that the sum of all probabilities is equal to 1.
From the given table, we know the probabilities for x = 0, 1, 2, 3, 4, and 5.
Adding up the probabilities for x = 0, 1, 2, 3, 4, and 5, we have:
0.64722784850823 + 0.29419447659465 + 0.0534899048353909 + p + 0.000221032664609053 + 4.01877572016461e-06 = 1
Simplifying the equation, we have:
p = 1 - (0.64722784850823 + 0.29419447659465 + 0.0534899048353909 + 0.000221032664609053 + 4.01877572016461e-06)
Calculating the missing probability:
p = 1 - 0.9999999999999989
p = 1.1102230246251565e-15
Therefore, the missing probability is approximately 1.1102230246251565e-15.
To find the missing probability, we can sum up the probabilities of all the known values and subtract from 1, since the sum of all probabilities in a probability distribution should be equal to 1.
Sum of known probabilities: P(0) + P(1) + P(2) + P(4) + P(5) = 0.64722784850823 + 0.29419447659465 + 0.0534899048353909 + 0.000221032664609053 + 4.01877572016461e-06
Sum of known probabilities = 0.994132036206047 (rounded to 15 decimal places)
Now, subtract the sum of known probabilities from 1 to find the missing probability:
Missing probability = 1 - 0.994132036206047 = 0.005867963793953
Therefore, the missing probability is approximately 0.005867963793953.