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Questions
Find the probability distribution of number of heads in two tosses of a coin.
If two coins are tossed simultaneously, write the probability distribution of the number of heads.
Solution
When one coin is tossed twice, the sample space is
{HH, HT, TH, TT}
Let X represent the number of heads s in two tosses of a coin.
∴ X(HH) = 2,
X(HT) = 1,
X(TH) = 1,
X(TT) = 0
Therefore, X can take the value of 0, 1 or 2.
It is known that,
P(HH) = P(HT) = P(TH) = P(TT) = `1/4`
P(X = 0) = P(TT) = `1/4`
P(X = 1) = P(HT) + P(TH) = `1/4 +1/4 = 1/2`
P(X = 2) = P(HH) = `1/4`
Thus, the required probability distribution is as follows:
| X | 0 | 1 | 2 |
| P(X) | `1/4` | `1/2` | `1/4` |
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- Find the total number of ordered pairs having one larger number.
- Let the random variable X denote the larger of two numbers in the ordered pair.
Now, complete the probability distribution table for X given below.
X 3 4 5 P(X = x) - Find the value of P(X < 5)
- Calculate the expected value of the probability distribution.
Five numbers x1, x2, x3, x4, x5 are randomly selected from the numbers 1, 2, 3, ......., 18 and are arranged in the increasing order such that x1 < x2 < x3 < x4 < x5. What is the probability that x2 = 7 and x4 = 11?
