Question

Pls help:)
A box contains 2 red cards, 3 blue cards and 4 yellow cards. Mary repeats drawing one card at a time randomly from the box with replacement until a red card is drawn. Find the probability that Mary needs at least three draws.

Answer 1

@kryton1212

Answer 2

thanks

Answer 3

The probability of drawing a red on any draw is \(p= 2/9.\)
The probability of successfully drawing a red at the kth draw is
$$
P(X=k)=(1-p)^{k-1}p
$$
The probability that at least 3 draws is required is
$$
P(X \ge 3)=1-P(X<3)=1-P(X\le2)=1-\left[ (p+(1-p)p\right ]
$$
Here we used the Geometric Distribution:

http://en.wikipedia.org/wiki/Geometric_distribution

Answer 4

Is this the full question?