A common discrete distribution is used in statistics, as opposed to a continuous distribution is called a Binomial distribution. The probability of at most 2 red cards is 0.5.
A common discrete distribution is used in statistics, as opposed to a continuous distribution is called a Binomial distribution. It is given by the formula,
P(x) = ⁿCₓ (pˣ) (q⁽ⁿ⁻ˣ⁾)
Where,
x is the number of successes needed,
n is the number of trials or sample size,
p is the probability of a single success, and
q is the probability of a single failure.
Using the given information the number of cards is 24 out of which 12 are red. Therefore, the probability of getting a red card is 0.5.
A) All red cards.
P(X=5) = ⁵C₅ (0.5⁵) (0.5⁰)
= 0.03125
B.) at least two red cards.
P(X≥2) = 1 - ⁵C₀ (0.5⁰) (0.5⁵) - ⁵C₁ (0.5¹) (0.5⁴)
= 0.8125
C.) At most 2 red cards.
P(X≤2) = ⁵C₀ (0.5⁰) (0.5⁵) + ⁵C₁ (0.5¹) (0.5⁴) + ⁵C₂ (0.5²) (0.5³)
= 0.5
Learn more about Binomial Distribution:
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