Question

Three red square pieces of wood, four yellow square pieces, and five blue square pieces are put into a cloth bag. Four red round pieces, two yellow round pieces, and three blue round pieces are also put into the bag. All the pieces are then mixed about. Suppose someone reaches into the bag (without looking and without feeling for a particular shape piece) and pulls out one piece.

Answer 1

The question is incomplete. Here is the complete question.

Three red square pieces of wood, four yellow square pieces, and five boue square pieces are put into a cloth bag. four re round pieces, two yellow round pieces, and three blue round pieces are also put into the bag. All the pieces are then mixed about. Suppose someone reaches into the bag (without looking and without feeling for a particular shape piece) and pulls out one piece.

What are the chances that the piece is red round or blue round piece?

a. Cannot be determined

b. 1 chance out of 3

c. 1 chance out of 21

d. 15 chances out of 21

e. 1 chance out of 2

Because:

a. 1 of the 2 shapes is round

b. 15 of the 21 pieces are red or blue

c. There is no way to tell which piece will be picked

d. Only 1 of the 21 pieces is picked out of the bag

e. 1 of every 3 pieces is a red or blue round pieces

Answer: b. 1 chance out of 3

              e. 1 of every 3 pieces is a red or a blue round pieces

Explanation: Inside the bag, there will be:

• Total of squares: 3 + 4 + 5 = 12
• Total of round: 4 + 2 + 3 = 9
• Total of pieces inside the bag: 12 + 9 = 21

The question is asking for a round red piece. The probability of that happening is

P(r) = $\frac{4}{21}$

And a blue round piece:

P(b) = $\frac{3}{21}$

It is a "OR" probability, so:

P(r or b) = $\frac{4}{21} +\frac{3}{21}$

P(r or b) = $\frac{7}{21}$ or $\frac{1}{3}$

Which means 1 out 3 pieces taken out of the bag will be red or blue.