A box contains three whole, two red balls, if two balls are selected at random find the probability that

a) one red and one white ball are selected
b) two of the same color is selected
c) no white balls are selected
d) no read balls are selected

Assuming your typo should say

.... 3 white, 2 red

prob(one red and 1 white) = C(2,1)*C(3,1) / C(5,2) = 6/10 = 3/5
or
could be RW or WR ===> (2/5)(3/4) + 3/5(2/4) = 3/5

prob(two of same ) ====> RR or WW
= C(3,2)/C(5,2) + C(2,2)/C(5,2)
= 3/10 + 1/10 = 2/5

prob(no white) ===> both red = C(2,2)/C(5,2) = 1/10
do the last the same way

answer

RESPONCE

To find the probabilities, we need to know the total number of possible outcomes and the number of favorable outcomes for each event.

In this case, the total number of possible outcomes is given by the number of ways two balls can be selected from a box containing three white balls and two red balls. This can be calculated using combinations.

a) Probability of selecting one red and one white ball:
The favorable outcomes here are selecting one red ball and one white ball. We can choose one red ball from two available and one white ball from three available. So, the number of favorable outcomes is 2*3 = 6.

Since we select two balls, the total number of possible outcomes is given by selecting any two balls from five available, which is calculated as C(5, 2) = 10.

Therefore, the probability of selecting one red and one white ball is 6/10 = 3/5.

b) Probability of selecting two balls of the same color:
The favorable outcomes here are selecting two white balls (C(3,2)=3) OR selecting two red balls (C(2,2)=1).

So, the number of favorable outcomes is 3 + 1 = 4.

The total number of possible outcomes remains the same (C(5,2) = 10).

Therefore, the probability of selecting two balls of the same color is 4/10 = 2/5.

c) Probability of selecting no white balls:
In this case, the favorable outcome is selecting two red balls (C(2,2) = 1).

Again, the total number of possible outcomes remains the same (C(5,2) = 10).

Therefore, the probability of selecting no white balls is 1/10.

d) Probability of selecting no red balls:
In this case, the favorable outcome is selecting two white balls (C(3,2) = 3).

The total number of possible outcomes remains the same (C(5,2) = 10).

Therefore, the probability of selecting no red balls is 3/10.