Question

2) A box contains 4 red roses and 5 white roses. If two roses are randomly selected without replacement (this means that when the first rose is removed it is not returned to the box), find the following probabilities:

a) The probability that both selected roses are white.

b) The probability that at most one white rose is selected.

c) The probability of not selecting any white rose.

Answer 1

Box contains 4 red roses and 5 white roses

Total no. of roses = 9

we will use the multiplication theorem which states for two events A and B : P(A and B) = P(A) P(B|A)

here P(B|A) is the probability B occuring , given that Event A has already occured

(a)

Probability that first and second selected roses are white =(Probability that first rose is white) * (Probability that second rose is white given that first rose is white )

Probability that first rose is white =

Probability that second rose is white given that first rose was white =

Probability that both the roses are white =

(b) Probability that at most one white rose is selected , meaning either no white rose or one white rose is selected in the two selection

Let Event A = at most one white rose is selected

Complement of Event A = Event A' = more than one white rose is selected or that both roses selected are white

According to complementary law ,

Required probability =  

(c) The probability of not selecting any white roses is same as Probability of having both red roses in both selection

Probability that first and second selected roses are red  =(Probability that first rose is red ) * (Probability that second rose is red  given that first rose is red  )

Probability that first rose is red =

Probability that second rose is red given that first rose was red =

Probability that both the roses are red =