A bag of contains 3 blue and 4 red balls. If 2 are selected at random: a. What i
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A bag of contains 3 blue and 4 red balls. If 2 are selected at random: a. What is the probability of selecting both red balls? b. What is the probability of selecting at most one blue ball? From the group of 140 baking at a local baking competition, 56 claim to be expert in pies, 66 in cakes and 58 bread. 12 claim to be expert in all three items, while 22 claim pies and bread and 20 claim cakes and bread. 28 claim to be expert in pies and cakes. Draw a Venn Diagram and determine how many claim an expert in none of the three. A five-card hand is selected from a standard deck of 52 cards. Find the probability the hand: a. Contains at least four spades. b. Contains 4 hearts and 1 club or 3 spaded and 2 diamonds. c. Contains all cards from the same suit. d. Contains at most one heart A large family lines up for a picture. How many ways can the 20 people stand in a line so that the 4 grandparents are always together??Explanation / Answer
A bag contains 3 blue and 4 red balls. If 2 are selected at random...
a. What is the probability of selecting both red balls?
Favorable cases: 4 red balls. So, picking 2 among 4 red balls is: C(4, 2).
Possible cases: 7 balls in total. So, picking 2 among 7 balls is: C(7, 2).
So, the answer is: C(4, 2) / C(7, 2).
b. What is the probability of selecting atmost one blue ball?
Of 2 balls, 2 possibilities: 0 blue balls, or 1 blue ball.
Just add these 2 cases.
0 blue balls is: the value obtained in the previous case, i.e., C(4, 2) / C(7, 2).
1 blue ball is: C(4, 1) * C(3, 1) / C(7, 2). (Picking one blue ball, and picking 1 red ball.)
So, the answer is: C(4, 2) / C(7, 2) + C(4, 1) * C(3, 1) / C(7, 2).
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