A pair of dice is thrown 4 times. If getting a doublet is considered a success, find the probability distribution of the number of successes.
Total number of outcomes = 36
The possible doublets are ( 1, 1 ), ( 2, 2 ), ( 3, 3 ), ( 4, 4 ), ( 5, 5 ), and ( 6, 6).
Let p be the probability of success, therefore,
Since the dice is thrown 4 times, n = 4
Let X denote the number of times of getting doublets in the experiment of throwing two dice simultaneously four times.
Therefore X can be take the values 0, 1, 2, 3, or 4.
Thus the probability distribution is:
X | 0 | 1 | 2 | 3 | 4 |
P(X) |
Using integration find the area of the region bounded by the parabola y2 = 4x and the circle 4x2 + 4y2 = 9.