If the probability of event A is 0.4 and the probability of event B is 0.3, what is the probability of both events occurring if both events are independent?
5.3 Multiplication Rule and Conditional Probability

Quiz
•
Mathematics
•
12th Grade
•
Medium
SHIRLEY Moe
Used 3+ times
FREE Resource
10 questions
Show all answers
1.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
0.12
0.5
0.25
0.07
Answer explanation
The probability of both independent events occurring is the product of their individual probabilities, so 0.4 * 0.3 = 0.12.
2.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
If the probability of rain on any given day is 0.2, what is the probability of no rain for 3 consecutive days?
0.6
0.3
0.512
0.8
Answer explanation
The probability of no rain for 3 consecutive days is calculated as (1-0.2)^3 = 0.512, hence the correct answer is 0.512.
3.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
If P(A)=0.6 and the P(B|A)=0.8, what is P(A∩B)?
0.2
0.25
0.75
0.48
Answer explanation
To find P(A∩B), use the formula P(A∩B) = P(A) * P(B|A) = 0.6 * 0.8 = 0.48. Therefore, the correct answer is 0.48.
4.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
A box contains 4 blue marbles, 3 red marbles, and 2 green marbles. What is the probability of drawing a blue marble followed by a red marble without replacement?
2/7
3/10
1/3
1/6
Answer explanation
The probability of drawing a blue marble first is 4/9. After drawing a blue marble, there are 3 red marbles left out of 8 total marbles, giving a probability of 3/8. Multiplying these probabilities gives 1/6.
5.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
If P(A)=0.7 and the P(B)=0.5, what is P(A∪B) if A and B are independent events?
0.9
0.2
0.3
0.85
Answer explanation
When A and B are independent, P(A∪B) = P(A) + P(B) - P(A) * P(B) = 0.7 + 0.5 - (0.7 * 0.5) = 0.85
6.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
A jar contains 10 red candies and 5 green candies. What is the probability of drawing a green candy followed by a red candy without replacement?
3/10
5/21
1/5
2/15
Answer explanation
The probability of drawing a green candy first is 5/15. After removing the green candy, there are 10 red candy out of 14 candy, then drawing a red candy is 10/14. Multiplying these probabilities gives 5/21.
7.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
A box contains 6 white balls and 4 black balls. What is the probability of drawing a white ball followed by a black ball without replacement?
2/5
4/15
5/15
3/10
Answer explanation
The probability of drawing a white ball first is 6/10. After removing one white ball, the probability of drawing a black ball is 4/9. Multiplying these probabilities gives 4/15.
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