A discrete random variable X can only assume the values of 0, 1, 2 and 3.Given that 𝑃(𝑋 ≥ 2) = 0.6 , 𝑃(𝑋 ≤ 2) = 0.85Determine 𝑃(𝑋 = 2)
Question
A discrete random variable X can only assume the values of 0, 1, 2, and 3.
Given that:
- 𝑃(𝑋 ≥ 2) = 0.6
- 𝑃(𝑋 ≤ 2) = 0.85
Determine 𝑃(𝑋 = 2)
Solution
To find the probability that X = 2, we can use the given probabilities P(X ≥ 2) and P(X ≤ 2).
P(X ≥ 2) is the probability that X is either 2 or 3. P(X ≤ 2) is the probability that X is 0, 1, or 2.
Since these two events overlap at X = 2, we can find P(X = 2) by subtracting the probability of the other events from the total probability.
P(X = 2) = P(X ≤ 2) - P(X < 2) = P(X ≤ 2) - (1 - P(X ≥ 2))
Substituting the given values:
P(X = 2) = 0.85 - (1 - 0.6) = 0.85 - 0.4 = 0.45
So, the probability that X = 2 is 0.45.
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