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Question 1 of 6
hard
There are 4 letters and 4 addressed envelopes. What is the probability that all letters are placed in their correct envelopes randomly?
Explanation: Total ways to arrange 4 letters in 4 envelopes = 4! = 24. Only 1 way has all letters in the correct envelopes. Probability = 1/24.
Question 2 of 6
hard
If A and B are independent, P(A)=2/3 and P(A∩B)=1/3. Then P(B)=?
Explanation: P(B)=P(A∩B)/P(A)=(1/3)/(2/3)=1/2.
Question 3 of 6
hard
A bag contains 3 red and 2 blue balls. Two balls are drawn without replacement. Probability both are red is:
Explanation: (3/5)×(2/4)=3/10.
Question 4 of 6
hard
A card is drawn. Probability it is a queen or a heart is:
Explanation: 4 queens +13 hearts −1 queen of hearts =16 cards. Thus 16/52=4/13.
Question 5 of 6
hard
For events A and B, if P(A)=0.8, P(B)=0.5 and P(A∩B)=0.4, then P(A|B) is:
Explanation: P(A|B)=0.4/0.5=0.8.
Question 6 of 6
hard
Two cards are drawn successively without replacement. Probability both are aces is:
Explanation: (4/52)×(3/51)=1/221.
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