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Question : 22
Total: 29
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.
Solution:
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,
p =
So, q = 1 - p = 1 -
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 take the values 0, 1, 2, 3, or 4.
P (X = 0) =
C 0 p 0 q 4 (
) 4
P(X = 1) =
C 1 p 1 q 3 (
) (
) 3
P(X = 2) =
C 2 p 2 q 2 (
) 2 (
) 2
P (X = 3) =
C 3 p 4 q 0 (
) 4
Thus, the probability distribution is:
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,
p =
So, q = 1 - p = 1 -
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 take the values 0, 1, 2, 3, or 4.
P (X = 0) =
P(X = 1) =
P(X = 2) =
P (X = 3) =
Thus, the probability distribution is:
| X | 0 | 1 | 2 | 3 | 4 | ||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| P (X) | | | | |
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