Question

In a large bag of marbles, 20% of them are red. A child chooses 14 marbles from this bag. If the child chooses the marbles at random, what is the chance that the child gets less than 6 red marbles?

Answer 1

Solution

Given that ,

p = 20% = 0.20

1 - p = 1 - 0.20 = 0.80

n = 14

Using binomial probability formula ,

P(X = x) = ((n! / x! (n - x)!) * p^x * (1 - p)^{n - x}

P(X < 6) = P(x = 0) + P(x = 1) + P(x = 2) + P(x = 3)+ P(x = 4) + P(x = 5)

=  ((14! / 0! (14)!) * 0.20⁰ * (0.80)¹⁴ + ((14! / 1! (13)!) * 0.20¹ * (0.80)¹³

+ ((14! / 2! (12)!) * 0.20² * (0.80)¹² + ((14! / 3! (11)!) * 0.20³ * (0.80)¹¹

+ ((14! / 4! (10)!) * 0.20⁴ * (0.80)¹⁰ + ((14! / 5! (9)!) * 0.20⁵ * (0.80)⁹

= 0.9561

Chance = 0.9561