43.3k views
3 votes
11. A bag contains 6 white counters, 7 black counters, and 4 green counters. What is the probability of drawing(a) a white counter or a green counter? (b) a black counter or a green counter? (c) not a green counter?

User Louissmr
by
7.4k points

1 Answer

5 votes

We know that the bag contains:

• 6 white counters,

,

• 7 black counters,

,

• 4 green counters,

,

• 17 counters in total.

We define the events:

• W = draw a white counter,

,

• B = draw a black counter,

,

• G = draw a green counter.

,

We have the following probabilities:

• P(W) = # white counters / total # of counters = 6/17,

,

• P(B) = # black counters / total # of counters = 7/17,

,

• P(G) = # green counters / total # of counters = 4/17,

(a) First, we compute:

P(W and G) = # white and green counters / total # of counters = 0/17 = 0.

The probability of drawing a white counter or a green counter is given by:


P(\text{W or }G)=P(W)+P(G)-P(W\text{ and G)}=(6)/(17)+(4)/(17)=(10)/(17)

(b) First, we compute:

P(B and G) = # black and green counters / total # of counters = 0/17 = 0.

The probability of drawing a black counter or a green counter is given by::


P(B\text{ or }G)=P(B)+P(G)-P(B\text{ and G)}=(7)/(17)+(4)/(17)=(11)/(17)

(c) The probability of not drawing a green counter is:


P(\text{not G)}=1-P(G)=1-(4)/(17)=(17-4)/(17)=(13)/(17)

Answers

• (a) P(W or G) = 10/17

,

• (b) P(B or G) = 11/17

,

• (c) P(not G) = 13/17

User Rolinger
by
7.6k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories