Conditional Probability Worksheet (Page 2 of 3) in pdf

11. A red and a blue die are rolled. Given that there is at least one six, what is the probability

that the red die is showing six?

12. Ten cards lie face down on a table. They contain the digits 0, 1, 2, . . . , 9. Two cards are

chosen at random from the table. Find the probability that

(a) the sum of the numbers is greater than 9, given that the ﬁrst number is 3,

(b) the second number is 2, given than the sum of the two numbers is greater than 7,

13. Two tetrahedral die are thrown; one is red and the other blue. The number on which each

lands is noted, the faces being marked 1,2,3 and 4. Find the probability that

(a) the sum of the numbers on which the dice land is 6, given that the red die lands on

an odd number,

(b) the blue die lands on a 2 or a 3, given that the red die lands on a 2.

14. Two cards are drawn successively from an ordinary pack of cards and kept out of the

pack. Find the probability that

(a) both cards are hearts,

(b) the ﬁrst card is a heart and the second card is a spade,

204

15. 90% of Scandinavians are blue eyed, whereas only 25% of English are. In our establish-

ment, 10% of the pupils are Scandinavian, and the rest English. I bump into a blue eyed

person in the corridor: what is the probability that he is Scandinavian?

16. A bag contains 4 red balls, 3 yellow balls and 5 green balls. I take two balls from the bag,

without replacement. Given that the balls are the same colour, ﬁnd the probability that

they are both green.

ry+gy

ry+gy+gr

17. A bag contains 4 red balls, 3 yellow balls and 5 green balls. I take three balls from the bag,

without replacement. Given that the balls are all the same colour, ﬁnd the probability

that they are all green.

18. A bag contains r red balls, y yellow balls and g green balls. I take two balls from the bag,

without replacement. Given that the balls are diﬀerent colours, ﬁnd the probability that

they contain a yellow.

ry+gy

ry+gy+rg

19. In a class of 24 girls, 7 have blonde hair, 5 have red hair and the rest have black hair. I

select a committee of 5 from the class completely at random. Given that exactly two are

red heads, ﬁnd the probability that my committee contains exactly one blonde.

154

323

20. A bag contains 5 white and 7 black counters. I take 12 balls from the bag with replacement.

Given that the ﬁrst 3 balls were black, what is the probability my hand contains equal

numbers of black and white?

0.08725

21. Two events A and B are such that P(A) = 0.6, P(B) = 0.2, and P(A | B) = 0.1. Find

P(B | A).

22. We receive 10,000 transistors from company A, and there is a 1% failure rate on their

components. We also receive 4000 transistors from company B, which have a 1.5% failure

rate. A transistor fails: what is the probability that it came from company A?

Conditional Probability Worksheet Page 2

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